I have found that hotels in London will drop the extra person charge for children, even those over age 12. If the website adds the charge when booking, I've had good luck writing to the hotel and receiving written assurances that the charge would be dropped. I did, at the Grosvenor House, have to show the emails to the desk clerk on check out in order to have the extra charge dropped.

Regardless of the charge, you still need to be certain that the room you book can accommodate three people. Check the maximum occupancy in the room description. That said, there can be exceptions to the listed maximum occupancy. I have had good luck booking a room at the rate I want (often on points), contacting the GM by email, explaining that we will be traveling with our child, and asking if they will be able to accommodate the three of us. In many cases they have assured us we would be upgraded to a larger room that would work (though in some cases it might mean accepting a stupidly expensive rollaway), or have said that a few of the rooms in the class we booked could accommodate us, and promised to make sure we got one of those rooms.