Hope this reply is not too late for you. I cannot help with costs too much because London was only part of our (two adults + 15yo + 12 yo) trip. Many of the London attractions have free entry (Madame Tusauds is a bit expensive). We were able to get pretty cheap accommodation (9 nights for Stg812 for a quad room with breakfast). The standard was not great, but we saw rooms for twice the price that were no better. By staying in the city we were able to minimise transport costs, an Oyster card gave us great flexibility and cheap travel. The food outlets near Kings Cross station were not great so that forced us into buying ready prepared meals from supermarkets like Marks and Spencer. Their food was pretty good and reasonably priced.