I stayed over a week at Piers apartment and it was really convenient - well located near st. James park tube, close to the many attractions and a few tube stations from almost everywhere. The apartment was as described, no surprises. we had plenty of hot water (although there was some challenge to handle the faucets to reach the right temperature). the kitchenette is indeed small but very functional and had all we needed. the bed is actually part of the one big room but could be separated by a curtain. in general the apartment, as many other centrally located apartments, is old, and the furniture as well, but this was fine for us. I think the combination of the price and location worth it.
Piers was a great host, very responsive and helped a lot. For example he took care to have a better wireless connection as soon as he understood this is important for me.
The building care-person is available for anything needed while you stay there so there is always a contact to talk with.
One comment is that we couldn't find a good grocery nearby. but we could find the basics at a store just around the corner, and two nice pubs just few meters from the building.
I recommend you to stay at Piers apartment.
Tsipi