Apparently the House of Westminster needs major refurbishment.
The BBC on the issue.
The Guardian on the same issue.
Or the official view point.
However moving out of London altogether could revitalise some area of the UK, just like Media City has done for Salford. It might also remove one of the real drivers of the pressure cooker London property market. That is also threatening the Greenbelt in much of the South East. Why not give a boost to somewhere elses property market? Its not as if London's will collapse, I don't see the financial institutions moving out (unless we leave the EU).
The sale of London property could even fund a lot of the cost of the move, and some of the House of Westminster could be kept for State and Pagentry occasions.
There is even a petition to sign here.