Hi
I'm in a very similar position to you - languages grad who worked in human rights/medical translation. I became interested in medicine about two years ago and since then have tried to get as much voluntary/work experience as possible. I studied for the GAMSAT and UKCAT over the summer and just sat them last month: the GAMSAT was pretty tough (I also have no science A-levels) but the UKCAT went well. I'm now just finishing off my UCAS applications for 2016 entry.
I'm sure you know this and it sounds like you're planning to do it anyway, but it's really important to get some work experience or volunteering in a clinical setting - not just for your application, but for yourself! I started out as a ward volunteer at my local hospital essentially to see if medicine really was for me, and I ended up really enjoying it and spending a whole year there. It was really helpful in deciding whether I had a realistic idea of what a medical career was like and if I actually wanted to be a practising doctor rather than continuing to work in human rights but with more of a public health focus, which was the other option I was considering. Since then I've done quite a bit of other voluntary work and work experience in paediatrics, mental health, and general practice. I'm not sure if it's enough to be successful this round, but the more time I spend on applications and the more work experience I get, the more I want to be a doctor, so I'm fairly relaxed about not getting a place this year and reapplying (especially if my GAMSAT scores are as dismal as I suspect!)
I don't think it's wishful thinking for someone from our background to apply - I know people who have got in straight from undergrad humanities degrees with little work experience, and others who have got in with science degrees and years of healthcare work. I think if you really want it, don't mind working hard, and appreciate that it might take some time, then you have a shot. Of course, remains to be seen how my apps turn out...I'll let you know how I get on! The only difficulty I have found is that as a humanities grad with no science A-levels, there are only a limited number of places I can apply. I'm from London, have lived there most of my life, and would really like to stay there, but as far as I can tell only SGUL will take me. However, I think if you really want to do it, you can't afford to be too picky about location...
Feel free to ask me any questions about how I've gone about studying/applying, although of course I can't yet confidently vouch for the success of my tactics! And good luck!
Elizabeth