how much does it roughly cost to learn? I assume it's more than normal if you're going to have an instructor with you?
First thing - gliding in the UK is volunteer led and run. Some lucky big clubs have paid staff - but most do not. The club is what you yourself put into it.
Unlike power flying - for most gliding clubs the instructors volunteer their time to help you learn the skills of flying. (There are paid courses but even then; for most cases the money goes to the club not the instructor). Clubs are all very different - some cover your years flying by the annual club fees with you only paying for the launch. Others charge you for the launch and a per minute hire rate. Some clubs heavily subsidize youth flying which you at 20yrs would be able to take advantage of.
How much does it cost? Depends where you draw your yard-stick; your age and ability with usually younger being better and at what skills level you wish to acheive.
I started gliding in Sept 2011 at 33yrs and from ab-initio to solo took two weeks (8 days with ~63 flights) and a total of £1200 + food/drink & fuel. I did two 5 day courses back-to-back at a major south-west English club.
Most clubs have a skills progression system that is based off BGA, FAI, and soon to be EASA rules. My club has "pre-solo white card", "post-solo white card", "red card", "yellow card", "blue card" which dictate the skills milestones. The BGA, FAI milestones are ab-initio, solo, bronze, bronze cross-country, silver etc...
For me to get from solo through the various cards to bronze cross-country took me approx. 22 months and something like ~£200/month give or take (not including the expeditions to Spain and Australia). However, to chase the elusive silver duration - I've probably spent over £800 in about 5 attempts... I blame the weather - but it could just be me :-(
Given that at your age your still classified as youth at most clubs - you'd probably spend about half that.
how many flights would you get a day? Are we talking one flight, 3 flights, or as many as you want?
Depends on you and the club... Some clubs have a strict 3 flights at a time to share resources and give the instructors a break. Other clubs allow you and the instructor to do what is safe. Some days I've only accomplished 1 flight - typically 3 - the highest within a day was I think 13.
if I started now, would I get much flying in over the winter, or is it more of a summer sport
Gliding is mainly a summer sport - but if you can deal with being on a freezing cold & windy airfield - best to learn in the winter and solo in the winter so you can start doing serious solo flights at the beginning of the summer season and work your way through the skills milestones as the soaring season improves. That's what I tried to achieve - and was reasonably successful in accomplishing that.
how long do your flights last (lets say for a general winter flight). Are we talking 5 minutes, 20 minutes, an hour
When learning - in the UK in winter at a flat-land site - expect training flights to last for 5-8mins. In Australia the training flights at the club my bother-in-law is learning at are an hour summer or winter...
two clubs near me ... (Both a fair drive away,
Most gliding clubs have on-site accommodation - some more plush/expensive than others. For the last few seasons at my club there has been a young female pilot that lives on the coast four+ hours away - she travels by public bus to the airfield - stays the two or three nights in the on-site accommodation - flys during the day - and then travels back home via public bus. I take my hat off to her for her dedication. There is nothing stopping you from doing the same - depends on your motivation.
What about Lasham ... They are the biggest in Europe, there should be someone of the right age etc there!
Any of the bigger clubs close to large population centers (and especially close to Universities) should have an active youth scene. Lasham has a youth corp - about 30 young people at full strength from 13 to 24yrs with 60:40 mix of genders. When the iGC and/or Southampton University group(s) are at full strength you can add another 12 young people. Over winter the youth corp are active Saturdays and so too are the University group(s).