In reply to rabbitlady9:
I'm across the pond, so some of what I say may not be fully relevant to the UK experience. At 74, I'm still actively climbing, but I started young 60 years ago at 14. At 36 you can still climb for many years, and your body will adapt to the task---that's what bodies do---so that isn't a concern at all.
Climbing gyms are a wonderful development and have made everyone far stronger. But indoor plastic is a very imperfect imitation of climbing, and I would strongly recommend getting an outdoor start, not simply because real rock is an incomparable medium, but also because the full spectrum of climbing experience encompasses far more than how to pull on holds, and you'll miss out on all that richness in a gym. Plus I think the "deep feeling" you refer to, which I am sure is authentic, has not been stirred by some genetic mutation that mysteriously draws you to overhanging plastic. Without allowing too much purple prose to intervene, you are feeling "the call of the hills," something as old and human as the race itself.
When I was starting out, that pretty much meant getting a rope and some gear and some books and a friend and figuring it all out by yourself, but nowadays there is highly competent and experienced professional instruction, and this is by far the most sensible route to take as an interested novice. Amortize the cost over, say, the resulting 30 years of climbing pleasure you get and it isn't even remotely expensive. Moreover, you get someone who knows climbing and knows the hills. At least in the US, the person teaching those beginner gym classes is likely to be be a teenager with little or even no outdoor experience who is following a script supplied by the employer and hasn't devoted any time and effort to thinking about what good teaching might entail and what sort of progression you should be exposed to.
All that said, gyms have become one of the social hubs of the climbing community, and joining a gym is probably essential if you want to meet other climbers. And yes, you will progress in terms of certain climbing skills and strengths much more rapidly in a gym than you could possibly manage outdoors. So I'd say sign up for the beginner gym class, but while you are waiting talk to some professional guides about what types of things might be possible for you this time of year. Obviously, for pure rock climbing, a summer start would be better, but some winter scrambling might still be possible---here I totally defer to local knowledge, as I am far away in completely ignorant of UK conditions.