To me, it seems as if your UKCAT is FAR too low to be considered for the grad entry programmes. You should be looking at getting scores of about 700+ which would give you a very good chance of getting interviews. This is also enhanced by your low GAMSAT score- you have 51, the cut off tends to be around 64 overall, the lowest I have heard for the overall cutoff is 59 and most GAMSAT unis require minimum scores in the subsections.
To not get interviews signifies that something is going wrong in your paper app and off course this problem is your entrance exam scores. I truly believe that if you can sort this out you should be able to get more interviews and from the interview, it is based on you as a person. I've also noticed that you have not got many replies from grad medics/grad applicants and as you know, grad entry is in a whole different ballpark to applying during alevels. It is not uncommon for grads to have to apply 3 times to get offers. (if you had applied 3x with alevels, then yes it would be a huge problem, but grad entry is so much more difficult to get into and the candidates are MUCH more stronger).
You are also not applying tactically and to highlight this, kings and brighton would require significantly higher ukcats (even in 2007) than what you had. In 2011 your gamsat was way too low and leicester require a year of paid healthcare experience to be able to apply to their gem - you were a hca but did you have this at the time. leicester get a lot of apps from the allied health professions - pharmacy, optom, podiatry, physio, paramedics who are all fully qualified healthcare professions at the time of the app and have already worked at least 1 year. 2012, again it should have appeared to you that if you got that sort of gamsat score and were rejected after interview the previous year, why the hell did you apply to swansea again? you were lucky to even get an interview at swansea with that gamsat, it's just too low so that was a wasted slot right there. even with gamsat of 61, it is doubtful whether you would have got a look in at all the other gamsat ones tbh. AAlthough your academics are good, they are not enough for cambridge - they often get people with straight As at gcse and a2, 1.1 degrees, Masters, PhDs etc and even people with those credentials don't get in - remember they are an acdemic medical school! Southampton is also one of the most competitive grad courses in the country because they don't interview. Again your UKCAT is on the low side for this school and tbh, I would not have applied there given your past luck so in my opinion 3 out of your 4 choices for 2012 were big mistakes. If you had chosen schools like hyms, peninsula (with a gamsat of 64 overall) you could have secured a better chance of getting to interview.
If you decide to apply again and it doesn't work out and you think you have done all you can and cannot sacrifice anymore time, that is when you leave it behind. Remember there are many more careers out there, medicine isn't the only one! Realistically i think you should give it another go but apply tactically and improve your admissions test.
So the 2 areas of improvement are 1) admissions test scores and 2) look carefully at the schools you are going for and whether or not you meet their criteria. You should resit the GAMSAT (51 is as good as nothing - why you used that 2 years in a row beggars belief, aim for 64) and then you can apply to st georges, notts, penisula (possibly swansea). if you get 64 you should be guaranteed an interview at all of those. i know i may have been harsh but this is the only way to get the message across!
EDIT - i've just reread that you were rejected after interview from swansea,leicester and uea in 2011. again you probably shouldn't have applied to swansea in 2012 - some medical schools have rules against this sort of thing in that if you are rejected after interview you cannot apply the following year but logic would suggest you shouldn't have applied there again.
because of those 3 interviews, my advice has changed. you have had a fair number of interviews now and things are still not going anywhere. if it is what you want to do then by all means apply 1 last time but to be honest i think you need to take a step back and have a good long think. medicine isn't the be all and end all. it is incredibly overhyped and there are many other satisfying things out there. have you ever considered other professions - pharmacy, teaching, nurse,optometry,dentistry? it is very easy to get strung up on medicine and keep on applying for it year after year and then get to a point where you realise that you wasted many years of your life going for this when you could have spent them more constructively. how about getting a day or 2 experience in eahc one of those professions i have mentioned and then if it interests you, go further. at fisrt you need to make a decision if you still want to be in healthcare or another profession. if it's healthcare look at the different options under that area - there are loads of things within the healthcare umbrella, medicine is just the one that the lay public hear about the most/ one that teachers push alevel students in most