London Bridge Station has recently been rebuilt to have a mezzanine style area. It's the 4th busiest in the UK with 61 million entries and exits.
St Pancras and Kings Cross were similarly rebuilt.
It is a bit complex to describe London Bridge to non-Londoners, but simply put, it was 15 or so platforms that were about 20ft wide and 12 carriages long, with nowhere to queue and trains every few minutes, on every platform (and it's a terminus, not a through-station).
A mezzanine in a central city for passengers to wait is an absolute necessity. Doubly so if the station is a terminus, which all of the major stations in London are (I'm not counting Blackfriars or St Pancras).
For the non-English readers, there is only one North-South through railway line in London (Thameslink), and only one East-West (-ish) (Crossrail) and that hasn't opened. All mainline stations in London terminate, and then you have to use the tube to connect to another.
Ultimately it's usage levels and capacity. UK stations don't have the capacity for the passengers, and often the capacity on the trains either.
It's simply one of the busiest stations due to its location.
The huge mezzanine in the other stations such as at Pershing is mostly wasted space however.
Take out the elaborate mezzanine and make it a simple single level multitrack platform directly under the surface, and you might make the first train and be out of the station in less time, lowering the needed capacity of the station structure in the first place.