First of all - Chin up. You are not a failure and you are probably just as good or better than a lot of medical applicants with offers.
Second of all - did you really want to do Medicine? The likely answer is yes, but the rejections will be making you doubt yourself. However I reckon you probably did really want to do it so lets not give up on that dream.
Thirdly - Rejections aside, you are in a quality position for next years applications for a number of reasons -
1) You can get some more work experience or preferably even a medically related job like a HCA (this is what I did on my gap year). This gives you so much to talk about at interview and just so much experience with patients and talking to other healthcare professionals. It gives you a great appreciation of what a hospital will be like to work in.
2) You have more time to research uni choices, write your personal statement, prepare for interviews etc.
3) You have the time to earn money for uni and to go abroad or do something crazy if you'd like.
4) Any offers you get would be unconditional
5) You get to ask for feedback on your application so you can avoid making any mistakes/improving on weaker areas of your application this time round.
6) Very few things show admissions tutors grit and determination for a career than re-applying after 4 straight rejections.
If I were you I'd first get straight onto trying to get a HCA job ASAP, you may not start until September, but seriously - start apply for jobs straight away because if your trust is anything like my local one it'll take a lot of time for the Human Resources department to plough through things!
Secondly, the obvious one - knuckle down and get good UMS grades, especially if you want to apply to Cambridge second time round. Definitely make sure you get all A's so you have your choice of every Medical School to apply to.
Thirdly, but most importantly - PLEASE, PLEASE, PLEASE do not call yourself a failure. I've been through exactly the same thing and it does knock the stuffing out of you. I applied to Oxford, St. Andrews, Bristol and Edinburgh first time round and I have to say I was quietly confident, I guess I wasn't really used to not succeeding at stuff, I had -
10A*'s, 3A's at GCSE, all A's at AS level (UMS around 90%), a good UKCAT (670 I think) and BMAT (21.2)
I got two interviews and four straight rejections.
However I refused to believe that I was inferior - it's easy to but please don't, for your sake, I'm sure you are better than that. It just so happens we are applying for one of the most competitive subjects there is. I'm not saying I should've got a place last year, I have faith in the admissions tutors that there were better people but the gap year I'm on at the moment has given me the advantages (that I listed above) that I think have given me better success this year.
I got my 4A's at A-level, did better in my UKCAT and BMAT, and got 3 offers and an interview (which I didn't go to!), including the Cambridge offer which I've taken.
I really can't encourage you enough to try to get back into gear, get your chin up and sieze the opportunity of this gap year. I didn't plan to take mine but I'm actually so glad I've done it now. The HCA'ing will just be so useful to me as a med student and beyond, and plus I get the chance to bugger off to China for 4 months (in less than 60 hours I might add, argh!).
Hang in there buddy, it does get better after the initial low, I promise you, and it can be done.
When Winston Churchill was invited to take a school assembly after WWII he got up onto the stage and all he said before sitting down again was this,
"Never, ever, ever, ever give up".