Riding from London
Hi there, you should be able to hire a bike from On Your Bike, on Tooley St nr London Bridge station.
A really good route that I did last weekend - cycling from London - is to go to Cambridge (about 60 miles, quite flat and beautiful countryside). Head for Springfield Park in Stoke Newington, follow the canal north for about 20 miles, then after that it's nice quiet country roads all the way to Cambridge train station where you can get a train back to Liverpool St.
Alternatively, get a train (from London Bridge) to somewhere like Sevenoaks, where there's some nice countryside and a few good hills. You could even follow some of the Tour route - there's a free guide to the Tour with all the routes coming out in The Guardian (who I work for) on Monday 2nd July.
Hope this is useful,