The Dive Scene in Britain is typically well governed, regulated and safety driven. The main groups of divers are Club, Company and Independent based. The BSAC organisation (club) has the lions share of dive operations in England, Wales and Northern Ireland. BSAC clubs dotted throughout the UK tend to encompass resident divers who live locally to dive sites in their area some are well funded and organised to travel to decent dive sites in UK overseas on dive trips.
BSAC dive clubs are a good idea for people wanting to learn diving who live nearby, most clubs have their own RIB and a towing vehicle to conduct dive local trips. BSAC clubs are run by Branch Officers (volunteers) at the week-ends and holidays when divers normally meet-up for diving and training activities. For this reason I wouldn't strongly recommend them if your after quick and no-nonsense diving (unless the club is resort organised - unusual for the UK). That said longer more drawn out training times and the benefit of mixing with the BSAC community almost always provides a wealth of knowledge and experience surpassing that of a short course with a dive company.
A good resource for getting in touch with a club in your area is the BSAC website.
Company based outfits or Dive Schools are there to make money from diving, its that simple. You pay, they provide. They tend not to have the ethos and 'esprit de corps' that typifies BSAC clubs. However they are often sharp, business-like and eager to keep the customer happy. The dive instructors are paid workers there to fulfil a role and this they do not take lightly. In the long term diving/training via a dive company is much more expensive than utilising a dive club but for folk with a short amount of time on their hands and a wish to sample the 'glamorous' UK waters then they can be good option.
The PADI website can locate a local organisation for your chosen area of diving.
So you've got Company and Club styles of diving but what about the divers who don't want to spend lots of cash on the Dive companies and/or live nowhere near a dive club. Well if you're already a diver you'll probably know this answer. Dive off your own resources. First you should be experienced enough to fully organise, plan and carry-out a days diving. You'll need all your own dive gear, plus an air cylinder (obviously!) and a means of getting out to the dive site which can vary from your own two legs to a fully fledged liveaboard dive cruiser!