Well, here's a quirky one for a kick-off:
How about getting a good filling meal along Oxford Street and then giving some blood down Margaret Street off Regent Street? Do your good deed for the day, and it last around 3 months (until you can do it again) and could save up to three people.
Make sure you make as much use of their free drinks and snacks while you're there - you've earned it! You could even do some shopping beforehand, and if you feel like treating yourself to a not so expensive beauty treatment afterwards, well then you'll helpfully find a well priced trainee beautician's place across the street from The Blood Centre. Around just £7 for a manicure, but make sure you book early. In one small area you could have eaten, shopped, given some blood and then had a little 'you' time. Simple. But not the most usual day out in London, no?