The following diagram is one I did using a plan from Higgs and Hill showing the cross-section of the tube tunnels. It will be seen the floating track section (marked in various shades of grey) is isolated from the main boxed structure. The black bits are the rubber bearings, about four inches thick. Its not shown on this diagram however this boxed structure too was encased within another boxed structure. The gap between the two would provide a sound barrier and prevent any noise from the trains transmitting upward and outwards.

The big problem with this specialist structure is it does not fully extend to those parts of the estate where there are residential dwellings. This is crucial especially at Brandon Mews, where it has been found the basement of this property and its foundations are undoubtedly stuck right on top of the tunnels without any sort of noise mitigation measures whatsoever. There is floating slab track in part of that section however its rendered ineffective by way of the structures not being isolated.
Lambert Jones Mews, at the west side of the estate nearest to Barbican station, has barely any noise mitigation measures, and its foundations/basement too is sited right on top of the running tunnels. The structure is at the start of the downward inclination from Barbican station so what this means is because there’s less depth below, the residential buildings are sat atop the tunnels themselves and those in lambert Jones Mews get an awful lot of noise and vibration too.
Defoe House, running lengthwise with the tunnels, which do get deeper at this point, does have special mitigation measures (a box within a box and floating slab track) however the structure is generating lots of vibration and noise perhaps because Defoe House is not transverse to the tunnel. I’m no expert but what I think is happening is because there’s so many structures on the same exact alignment (its a boxed railway tunnel inside a boxed structure, which is also inside another boxed structure, inside yet another boxed structure) well its become like an amplifier that increases rather than decreases the sound and vibrations form the trains.

Gilbert House is the one on stilts, but they can feel the vibes from the trains below the lakeside terrace. Even as I stood here I could feel them too!
Gilbert House doesn’t get the noise nuisance like the others do, but it still gets vibrations form the trains and this result is because although the building is placed on stilts high above the Barbican lake, the vibrations from the trains finds their way up those stilts into the residential flats.
The Barbican is all concrete and steel construction, evidently a dense material and a good conductor of vibration and noise. The planners must have known this when they drew up the designs for the Barbican and that is why they stipulated a special construct of track and tunnel.
Very strangely they didn’t afford that luxury for some parts of the estate. Why? The only thing I can think of is the planners had thought the huge Barbican lake would act as a noise barrier, or at least soak up any potential noise coming from below, which it does to an extent. The lake is extremely shallow however (perhaps no more than half a metre deep) so its not that good as a sound dampener anyway. Very unfortunately the lake does not cover those parts of the estate with some of the worst problems.

Great pic showing the new Met/Circle tunnels where the track diverges! The year is possibly 1966/67. Source: Historic England
The picture (above) of the surveyor by the tunnels is of great interest. This is just past the end of the present Moorgate platforms. The top of the tower of St. Giles Cripplegate – which is the church in the middle of the Barbican estate – can be easily seen. Just behind the photographer would be the present alignment of Moor Lane. The east to west crossover at the end of the platforms can be seen behind the surveyor. Above the air space directly would be nowadays be Willoughby House and that behind the surveyor Brandon Mews. The concrete structure seen here above the roof of the train will eventually become the bottom of the Barbican lake!
In a nutshell this construction picture does explain why those in Brandon Mews get the worst from the tube trains. Its because this is where the tracks diverge for the Moorgate terminating platforms. There’ll be a constant thump thump noise as the trains pass over these points. Remember its not just trains terminating here but also the through trains. These too have to pass over the points that lead to the terminating platforms. In the peaks its probably practically every minute or two, that a train thumps their way through these points causing misery for the residents above.

2020 picture looking down the tunnels to the crossovers. The junction for the Moorgate terminus platforms can be seen in the distance heading off to the left.
In the image above, the cross is where our guy would have stood as he undertook his surveying work in the 1960s! In the immediate distance above the crossovers would be Brandon Mews, one of the worst affected Barbican properties. It can be that seen the tube dives under the Barbican lake before rising again beneath Defoe House to reach Barbican station. The same bit of concrete structure seen in the sixties photo can also be seen in this one I took! Eastbound trains have two sets of points to clatter through, whilst westbound trains have three sets of points they clatter through.
The other issue is the tracks rise up at this point because they have to reach the Moorgate platforms. What that means is the tunnels are not so deep as the remainder and it obviously meant Brandon Mews had to be, as it were, bolted straight onto the top of the tunnels.

A perspective from the other platform at Moorgate – showing the trailing crossover which could be superseded by that at Liverpool Street.
There are six points in this section alone. Two of those within the through Moorgate platforms are perhaps not so crucial, but it means there’s five sets of points through which trains continuously clatter their way. This is why the intrusion at Brandon Mews is much worse than that at Lambert Jones Mews.
Track relaying took place last year to mitigate the worst of the problems on the west side of the Barbican which should resolve the issues to an extent for Lambert Jones Mews and Defore House.

A rare picture showing the top of the railway tunnels where the lake is sited. Their alignment can clearly be seen. A short section on the right and not yet built over belongs to the Met/Circle/Hammersmith lines. The photograph was probably taken in 1969. Source: Collage

The tunnels are evident in this view from presumably early 1970. Source: You Tube
In terms of the above image Gilbert House is in the middle. Its said the first occupations here were in August 1969. On either side can be seen the cross members supporting the boxed sections around the tunnels themselves. Those on the right side clearly have a thin sheet of water (probably from rain) on the top of the boxed sections themselves. Compare this with the earlier picture and it will be seen the inner boxed sections had not yet been completed. The Barbican Centre and Guildhall School of Music & Drama had not by this time started construction which explains why the tunnels were in a still partially incomplete state.
If one wants a real good look at the alignment of the tunnels as they were then, here’s another picture….
The tunnels – with the cross beams evident which were used to roof over this section and form the lakeside terrace. The contractors’ mess rooms and staff facilities can be seen sat on top of the tunnels. Source: Financial Times
One can see from this image how these tunnels just pass beneath part of the Barbican Centre itself. It also shows how the tunnels clearly go straight underneath Defoe House. Again I would think this picture is perhaps 1969-1970. Its clear this half of Gilbert House has no residential occupancy yet. The same goes for Defoe House which still seems to be in a state of construction. The fact this side of Gilbert House (and Defoe House) were not complete at this moment in time is perhaps why complaints about the noise from the trains did not start until the seventies.
The first report of riding quality and generated noise on the new sections of line seemed very favourable with the observation that train riding was much quieter than usual, though it was said a speed restriction was in operation at the time so it was not possible to say with complete confidence whether the new type of floating track had achieved its objective.

The first ever observation on the riding/noise quality of the new tube line though the Barbican development. Source: LURS Jan 1966.
On that basis it can be assumed that depite the new tunnels opening in 1965, it as not until the first residents moved in these parts of the estate (early/mid-seventies) that the issue with noise coming from the trains was noted.
So why is it that the trains through the Barbican have got noisier?
Despite the apparent effectiveness of the floating slab track (which hasn’t really been that effective as the problem has perpetuated for more than fifty years) what is now happening is the S7 and S8 stock are somehow causing the dampening properties of the slab track to fail (in other words to become more amplified.) Remember it was said the problem was not so bad until the S7 and S8 stock came along?
There is a difference in the types of tube trains used. The C69/77 tube stock and the older A stock were both 16 metres long (14 for the C69/77 trailers.) The S7 and S8 stock is 17.44 metres (15.44 for the non driving cars) thus it may be the differences in length that is causing the floating slab track to react differently.
Here’s TfL’s explanation re the new S7/S8 tube stock and tube noise. They say no regular in-train monitoring of any sort is undertaken.
Another factor could be the modern floating slab track requires the rails are fixed directly to the slabs with special fittings and mounts etc. That in the Barbican is classic track formation (rails, sleepers and ballast) laid on top of the floating slab track, so there is possibly another factor here. These days no-one would think of building floating slab track and then putting a classic railway track formation (with sleepers and ballast) on top of it!
Thus we know despite the advanced technology used in the sixties, the mistake was to build the track formation as a classic one. Not as how it would be built these days.
The modern suspension of the S7/S8 stock likely does not work so well with this older and very unusual type of track formation. Not only that the bogies are somewhat further apart between the different units (compared to the older tube train units) thus there’s a different weight distribution downwards which is causing the floating slab track to react differently. I’m no rail engineer hence these are just ideas as to what could possibly be happening.