If you're looking for a day out of London, why not head to the university town of Cambridge. After only 45 minutes on the train, we were wandering around the streets of historic Cambridge. It took us a while to find the nice bits, as much of the main street was infested by high street shops and unfortunately made it look like any other town in England. But once you head over to the riverside where all the old colleges are, you'll understand the appeal. Amongst the most spectacular colleges that still exist, check out Peterhouse, which was founded in 1284, and Kings College that has an impressive chapel where you can catch a choir concert.
Getting to the slow travel bit... You can rent bikes at Cambridge station which I would highly recommend as it's a very bike-able city (if the thousands of bikes around the city are anything to go by). It reminded me of a Dutch city. Alternatively you can make your way to the riverside at Mill Lane Boatyard and rent a self-hire punt to go punting along the river. This is THE Cambridge thing to do and seems like a lot of fun, especially if you're in a big group. Then either cycle, punt or walk to Grantchester, a lovely little village 3 miles from Cambridge. Grantchester is a tiny village with thatched cottages, a few good pubs and the highest proportion of Nobel prize winners.
If you're opting for the walking option, I'd recommend walking through Newnham and stopping along Grantchester meadows for a picnic. Then once in Grantchester, treat yourself to a nice pint at the Red Lion pub or traditional tea at the Orchard in the garden.