London isn't as pricey as it seems, if you are flexible. For example, for 1 million US you can get a modern 100sqm apartment in places in zone 1 or 2 in London e.g. Clerkenwell, Camden, Islington, Fulham etc. These are walkable to the centre or have quick public transport, are pretty safe, have plenty of decent bars, restaurants and clubs etc.
My views on space - single person only needs 50-60sqm, and 70-80 is a luxurious amount of space. Cohabiting couple need 70-80, and 90-100 is luxurious. Since property is so expensive, it is better to keep space as small as you can handle. Most people get too much space, then don't use it - they just fill it with clutter. I found that living alone even in an 80 sqm 2-bedroom apartment, I rarely used the 2nd bedroom. I once lived in a 90sqm house and 2 of the rooms I hardly ever used. Bedroom, living room, kitchen, bathroom is all you need for 1 person - get a spacious living room and put a corner desk and a laptop in the corner, and you have a home office too.
Finally, as an expat trader/investor I would always rent rather than buy. Transactions costs for property are huge, as an expat you are far less tied to one place, you have foreign exchange risk, and mortgage finance is more difficult to find and more expensive. Finally, in international centres, renting is usually very cheap compared to owning.