24 hours in London...

It would be worth getting to Buckingham Palace for the changing of the Guard.
http://www.changing-the-guard.com/dates-times.html

As your time is so short I would plan your iternery and journeys in advance using the www.tfl.gov.uk journey planner to get as much done as possible.

There are lots of Starbucks around London and the bespoke offer where you get a £10 voucher for £5 is still on. I know Starbucks is not cheap but for the £10 you could get a frap or hot drink and cookie/cake each.

Curently wowcher have a hop on and off London bus tour offer for £4 a child and £7 and adult. Don't know if it is any good but seems to be a lot of people have bought the offer.
http://www.wowcher.co.uk/deals/london/deal-56071-detail/4-instead-10-child-ticket-bus-tour-london-7-adult/deal.html

The Albert Hall is literally a 10 min walk from the Science Museum, Natural History Museum and the V&A. All of which are FREE.

Along Kensington Road is the American Whole Foods Market. It has a fab deli, cheese room and clean loos! If it is a nice day you could pick up a really nice snack and sit next to the Albert Memorial in Kensington Gardens.

http://www.wholefoodsmarket.com/stores/kensington

I would strongly advise getting a London map. I know you are only there for one day, but getting around is so much easier with a map. And the map lasts forever.