Google the Royal College of Ophthalmology, think they have an online guide to laser eye surgery that may be helpful.
Make sure you meet the surgeon who will be operating on your eyes, NOT some sales assistant or 'patient adviser'. Ask them how they carry out the procedure, what techniques/equipment they use and about before and after - what sort of aftercare is on offer? What happens if you are not happy with the results or have any complications?
Check out the surgeon's qualifications and experience - are they a bona fide ophthalmic surgeon, are they on the GMC's specialist register and do they carry out lots of laser eye surgery procedures? (No use seeing an ophthalmic surgeon who mainly does something else and only a handful of laser eye ops every other week.)
Make DOUBLY sure that the surgeon takes you through their own outcomes data for surgery on people with the same prescription as you - no use the surgeon saying 'oh yes, 95 per cent of my patients have an improvement of X amount' if a significant proportion of those patients are unlike you - if there are lots of severely shortsighted people of -10 and you are only -2 or the other way round.
Worth meeting a few surgeons before making up your mind. Avoid anywhere that isn't happy for you to meet the surgeon, and any surgeon who isn't completely happy to answer detailed questions and show you their outcome data.
Oh, and avoid anyone who pretends none of their patients have ever had any complications. That won't be true. Or claims that the only complications anyone ever has from laser eye surgery are minor. That's not true either from the patient's point of view. Being left with poor night vision to the point where you can't drive after dark is not unknown, and glare and haloes may sound minor but not if you have to live with them permanently.
There's an American surgeon who is well-regarded (but I haven't had any procedures there so can't vouch for him from personal experience) who runs a clinic called The London Vision Centre - they used to produce a Guide to Laser Eye Surgery which had lots of questions you may want to ask and information about relevant qualifications/different kinds of procedures. May be worth a google.