I used Medics on the Move (you don't have to be in the medical field to use them, though -- we weren't). My agent was Louise Thompson, and she operates out of the Newbury/Reading area about 35 miles out of London. Which means that she may do London too, I just don't know. And if she doesn't, probably someone else in her organization does. We paid 450 pounds (about $1,000).
She was such a help! She drove us all over the place to view properties. We never would've been able to find all of these places being new to the area, and not to mention being confused by British driving. She also helped negotiate the lease and came with us when we moved into the flat to make sure we knew how to use all the appliances and such. We didn't need the service of having her check out local schools, but she does that, too. She also helped us flee a horrible B&B a "friend" recommended to us and found us a lovely, quiet, low-cost place when we first arrived. And she drove us there, she set up a meeting at a bank and drove us there so we could set up an account. It was costly, but she earned her money!