In reply to Tony the Blade:
Indoors:
Bouldering at Kelsey Kerridge, can get a bit crowded and not really a dedicated wall, but it's local.
There's a few small top-rope walls attached to local schools / colleges, but access is difficult
Otherwise head to Big Rock Milton Keynes (~1 hour away), Harlow (~1 hour away), Peterborough (~1hour away) or Stowmarket (~1 hour away - seeing a trend here?)
Outdoors:
There's a few small venues like Sawston bridge for bouldering, but mainly you're looking at a long drive. Get used to driving / being nice to climbers with cars.
Peak District can be done in a day trip 2:15 (South East) minimum trip time each way
Wye Valley can be done just in a day trip, nicer to make a weekend of it.
Shameless plug - look at the Cambridge Climbing and Caving Club website for the 2016 calendar (
http://thecccc.org.uk/calendar/ ) for as-organised-as-I-can-make-them trips.