Here's what the National Careers Service says:
https://nationalcareersservice.direct.gov.uk/job-profiles/massage-therapist
You'll see that there's a link from that page to the website of the Sports Massage Association. Taking a look there shows that there are currently only three accredited training providers in the UK. However one of those providers is Cardiff Metropolitan University, so that would seem likely to be your best option:
http://www.cardiffmet.ac.uk/schoolofsport/courses/Pages/Sport-Conditioning,-Rehabilitation-and-Massage-BSc-(Hons).aspx
If you can't commit to a full degree course then you might need to travel to Brighton to complete all of the modules for the ACMT certificate from Jing. You could either do that over an extended period of time or you could do the whole lot in one go throughout August:
http://www.jingmassage.com/massage-qualifications/certificate-advanced-clinical-massage/
(However you can't take that course until you've undergone initial massage training first).
The only alternative (for an SMA recognised qualification) would seem to be the Oxford School of Sports Massage:
http://www.ossm.co.uk/
However a parallel body to the SMA appears to be the Institute of Sport & Remedial Massage:
http://www.theisrm.com/index.php
One of their course providers is near to you, in Bristol:
http://www.themassagetrainingschool.com/
As you state, there are lots of other companies offering all sorts of courses but there would seem to be little point going on them if the certificate you end up with isn't recognised by employers. You need to be aiming at either a degree or a Level 5 BTEC qualification.