My mind can't compute supporting another team in any situation. I'd sooner stop watching all football than support a different side.
In a scenario where I was born in London and somehow had the choice of picking my team from birth based on the opinions I currently have, West Ham would probably to be the standout pick.
I do have respect for fans of the smaller teams in London though, it's far easier to just be a chelsea fan rather than a qpr or brentford fan, easier to pick west ham over say a Charlton, or arsenal over Leyton orient etc.