Either you're one of those super-privileged people who live close to the center of London and Paris
You have no idea about London.
When I was a student I lived 15 minutes walk from St Pancras International Station. Immediately north of the station used to be really bad, but since its redevelopment (The Guardian / Google offices etc) you need to walk a little further -- about 10 minutes is plenty.
Council (social) housing on all sides on Copenhagen Street, 0.7 miles from trains to Paris.
The main local issue for the area is the expansion of one of the stations, which is criticised because an area of council houses behind the station would be demolished.
(Incidentally, I live relatively close to LHR, it's about the same time by public transport to either that airport or St Pancras. I'd still prefer the train if I'm going to Paris.)
You might be correct in 10 years or so, if the new government's desired changes to the way social security is paid are fully implemented. (Poor people will no longer be allowed to live in inner London, and the state-owned housing will be sold off.)