In reply to OliBangbala: Blimey - no idea why people are suggesting North Wales. It is probably just as quick to get to Chamonix by that measure!
You can get the bus from town out to the Chew Valley which gives you access to Dovestones, Wimberry, Standing Stones, Robs Rocks and much more.
The Eastern Edges are very easy with a train trip to Hathersage or Grindleford which gives you Stanage, Froggatt, Burbage and Millstone Edge to name but a few.
If the train to Hathersage is a bit dear, you can cut your losses and get off at Edale which gives you access to the Kinder plateau and if Edale is too dear, you can get off at New Mills and head to the Tor there.
You can also get the train to Walley Bridge and cycle / long walk up to Windgather or to Dove Holes for Castle Naze. The train to Buxton also gives you Harpur Hill.
Failing all that, once you get out into the sticks it generally isn't to hard to cadge a lift as long as you aren't covered in mud or soaked to the bone.
In other words - save your pennies before you start heading to Wales or the Lakes.