All of the national museums and galleries are free. You could easily spend a day just visiting the South Kensington 'big three'. (Science Museum - great for anyone who's still akid at heart. Natural History Museum - a bit stuffy in places but with some great individual galleries. V&A - frequently overlooked but absolutely stunning). Similarly, the British Museum, National Gallery, National Portrait Gallery and many other attractions are also free. It also costs nothing to view the Changing of the Guard, stroll through Hyde Park, listen to the opera singers in Covent Garden Piazza or watch the fountain displays in the courtyard of Somerset House.
If you're planning on seeing the main sites, you'll only have to pay for places like The Tower of London, St Paul's Cathedral, Maritime Greenwich or Hampton Court (if you venture that far out). They're all fairly expensive. (The Tower was �15 the last time I checked) but, combined with the freebies, it's unlikely that you'd visit more than one (or, at most, two) a day.
I know that I don't need to tell you about Bistro 1 but there are plenty of other reasonably-priced places for food if you look around a bit.
�150 should be ample.
Chris