Professor John Burland of Imperial College London said work on the London Underground Jubilee train line in the 1990s had not caused dramatic movement, while a spokesman for The House of Commons commission said the tilt could have existed since its construction in 1859.
Burland said "When I first started work on the car park it was obvious that it was leaning. It was probably developed at a very early stage because there's no cracking in the cladding and we think it probably leant while they were building it and before they put the cladding on.
"There's no such thing as an old building that isn't cracked. In fact they're beneficial because the building moves thermally more than is caused by the Jubilee Line and the movements concentrated around the cracks and, if they didn't, there'd be cracking elsewhere.
"So these have been there for years and they're certainly not caused by the Jubilee Line or the car park."
Ianvisits has a great blog post from a number of years back about the Jubilee Line tunnels under Big Ben's clock tower.
He wrote "As a Jubilee Line tunnel was tunnelled by the tunnel boring machines (TBM), despite the best efforts of the workers, there is always a slight gap between the tunnel wall and the soil outside, leading to some subsidence at ground level. The gap is only a few millimetres, but when amplified around the entire tunnel diameter, that actually adds up to quite a bit of missing soil, and can cause significant problems. Before work starts on any tunnel now, ground surveys and measurements are taken to calculate the subsidence risks and effects on buildings."
"The big risk, which was gleefully latched onto by the news media was that the tower would start to lean sideways towards the tunnel work and may even start to develop cracks or damage. As the TBM worked its way through Westminster, electronic monitors on the tower checked how far it was starting to topple, and then pumped grouting into the soil to basically push the tower back upright again."
His post has more pictures of the compensation grouting work ( from a talk on tunnelling by the Royal Society) which was only carried out at night. He concludes "Without compensation grouting, it is expected that the tower would have tilted by some 10cm at the top – which would have been obviously unacceptable."