If you believe London's Evening Standard (not the most reliable of newspapers) in expensive areas of London it's common for people to buy 19th century mansions then build underground "mega-basements" [1,2,3,4] with features like pools, tennis courts and classic car museums.

So it's possible. It may be expensive.

[1] http://www.standard.co.uk/news/london/kensington-digs-in-wit... [2] http://www.standard.co.uk/news/london/daimler-heir-wins-figh... [3] http://www.standard.co.uk/news/london/billionaires-chelsea-b... [4] http://www.standard.co.uk/news/london/tetra-pak-heir-hans-ra...