I used to live in Kew (rented) and the Richmond area sure is nice, but as expensive as anywhere in the country, probably. Try a Rightmove search for postcode TW9 (upto a mile radius, say) and see what comes up. I cannot see vendors in this area being too flexible (i.e. in terms of lowering price) - due to a strong London market and it being a desirable area
There are one bed flats coming up for this price range (£200,000) but you may be better off finding somewhere further out to get more bang for your buck. I don't know what Brentford is like (???) - but Rightmove reckons its within a mile of TW9 and there are plenty of flats for sale there. As I say, I don't know what its like as a place to live or in terms of transport links.
There is actually a 1 bed flat in Chiswick listed there for £199,999, St. Thomas Road, W4. (Search TW9 with 1/4 mile radius)....