The Changing of the Guard, at Buckingham Palace, only takes place on alternate days at this time of the year. During January, it occurs on even numbered dates. There's an alternative ceremony, which takes place daily at 1100 (1000 on Sundays at Horse Guards Parade).
How much should you take for food? That's one of those 'how long is a piece of string' questions. There are plenty of cheap places to eat in London but there are even more places which are trying to rip you off. (Watch out, particularly, for take-away and 'eat in' price differences. Lots of places will offer you a tempting slice of pizza, to take away for, say, �1.50. However, when you order the same slice of pizza inside the caf�, it comes with a small amount of salad and the price goes up to �4).
As I suggested above, I think the best bargain for food is the Bistro 1 group of Mediterranean-themed bistros. (I always go to the one in Southampton Street, by Covent Garden but there are another two branches in Soho). A really good 3-course lunch will cost you just �7.50. The menu is here:
http://www.bistro1.co.uk/Bistro1%20Lunch%20Men u.pdf
Other information is here:
http://www.bistro1.co.uk/
If you're on a really tight budget, there are plenty of places selling cheap sandwiches to take away. (Perhaps you could have lunch at Bistro 1 and then just buy sandwiches to take on the bus back to Coventry?).
If you're going to the Natural History Museum, I recommend also visiting the V&A, which is just down the road. It often seems to be ignored by visitors to the other museums at South Kensington but it's a wonderful place to explore.
Chris