We took this tour in February. All breakfasts are covered, and about half your dinners or big lunches. We ended up spending less than $50 a day for the two of us, while on the tour itself. So yeah, 150 GBP would probably be just fine for one person. It is possible to eat cheaply in London if you're careful, but a couple of the dinners we had were pricey. So bring a debit card, in addition to your credit card. Let your bank know when and where you'll be so they can unblock it, and you can replenish your cash reserves at the cash points (ATMs). And pay attention to the post suggesting you wait until you get to England before getting pounds. Since you have a Oyster card, you don't even need cab fare to the hotel.
There is plenty to do in London that doesn't cost much. Walking is free, the parks are great, and most of the museums are free. But, as always, YMMV.
And by the way, this is a wonderful tour. We loved every minute of it. It is one of the busier tours, though. We had less free time than we would have liked, but that's okay; all the more reason to plan a return trip!