If you've made it to St James park, then you're just a stroll from Horseguards Parade, Trafalgar Square, Big Ben and the Embankment, where you can go and watch the biggest bicycle wheel in the world revolving slowly...
British Museum currently has the Terracotta Warriors, although tickets sold on the day are limited, so you might miss out on those...
If you made it all the way down Oxford Street (ugh!), you could turn into Regents Street and do Hamleys, if you're the sort of person who's never grown out of toy shops.
It depends how much you like walking though (and how comfy your shoes are). I've done some marathon strolls (well, ok, not actually marathon as in 26 miles, but long) in London, just by virtue of wandering from sight to sight. One of my best memories ever was doing Tower of London to King's Cross, via the Tate Modern, St Pauls, Fleet Street (I think) and a detour down Oxford St for Sushi. Took all afternoon mind, but did include a couple of drinks in a pub along the way...