I'm not actually a skydiver, but i did a lot of research last year (tempted to start this term, but gliding takes precedence

)
The cheapest way to learn is the RAPS (Ram Air Progression System). Prices start from £320 for the intial training and then £40-50 per jump thereafter. You start at a fairly low height and get chucked out of a plane with your chute already open. You do this a few times, getting more confident in the air and slowly you build up to freefalling (starting with 5 secs and the chute auto-pulling, to you pulling, to longer time, etc, etc). It takes a while, but it's fairly cost effective.
The expensive and more intensive route is AFF (Accelerated Freefall). It's only 8 training levels plus 10 consolidation jumps, but you start freefalling from the start with two instructors. You build from there and are able to go solo after 8 and you simply do your consolidation jumps for the equivalent of "hour building" to get the license. Cost is generally around £1500-2000 and there are quite a lot of places you can do this outside the UK.
Skydiving is one of the few aerial sports that won't suffer too much if you learn in a country where it's sunny nearly every day of the year (like Spain), so it can be cost effective and more fun to go somewhere where the skies are clear and blue.
If you're a student things are a bit easier, just join your local clubs. Warwick has the largest skydiving club in the country, and Soton is pretty large too - as a result you can get very good deals on jumps/training.