We haven’t established that you’ve ever been to London.
You can buy a house in outer London for 800k - Worcester Park, Enfield; you can buy a house in a scruffier area of inner London - some parts of E, SE, etc; or you could buy a very small house in smarter area of inner London - but hard to find.
Figures for the last year:
Overall average of house prices in Central London was £1,278,384. Right Move.
Terraced properties in Central London average of £3,231,286. RM
Detached properties in Central London average £2,783,333. RM
Average price of terraced house SW London was £976,000 - £1.3 million RM
Average price of detached house SW London was £2 - £2.6 million+ RM
Average price of terraced house NW London was £902,810. RM
Average price of semi-detached house NW London was £957,425. RM
Average price of detached house NW London was £1,877,009. Zoopla
Average price of terraced in W London was £1,599,976. RM
Average price of semi-detached house average was £1770,897. RM
Average price of terraced house in EC London was £1,242,500 RM
Average price of Semi-detached house in EC London was £1,500,000. RM
Parts E & SE London are cheaper as I said. Excluding areas such as Hackney, Blackheath, Dulwich which are in line with above.