Just to chime in with Pitlamp:-
I learnt to dive in 09/10 with a BSAC club, after 6 yrs caving. The CDG was always in the back of my mind, but I agree with Pitlamp & keep your own counsel & just learn to dive with the open water club at first. You might not even like diving, or find you have physiological issues that make clearing your ears difficult + painful without surgery.
BSAC is perhaps slow, but usually the clubs run on a yearly training cycle, starting in the Autumn with pool sessions + theory lectures over the winter, followed by the open water lessons in spring ready for the summer dive season. So you sort of enter at one end & you'll be whisked along. And cheaper, as you're not paying the instructors. As the clubs are run by volunteers they are extremely variable in activity and quality of the teaching.
Sea / wreck diving is surprisingly expensive - boats are massive holes in the ocean into which money is poured. It's great fun but not massively relevant to UK cave diving, except for an easy way to get deep-ish experience & hone your buoyancy skills doing deco.
However, shore diving I find is extremely similar to UK sump diving, and cheap as a result of the relatively low gas consumption (small bottles, no need for nitrox, wetsuit acceptable) + lack of having to pay for a boat.