I agree with everyone here, changing pills shouldn't be a problem, and once you do find one you like you'll probably stick with it for years, so its a hassle now but will pay off! I was on Yasmin (I suppose it must be called Jasmin in the UK), and I had bad migranes on it, but it is supposed to be one of the better ones in that respect.
Also, you should talk to your doctor about trying some non-pill methods. I used "nuva ring" for a while, it is just a piece of plastic you position inside you, and because it releases only localized hormones it is supposed to cause fewer side-effects. You can also take it out when you are not sexually active to further reduce problems (I think you have to have it in you for 12 hours before and 12 hours after sex, I don't remember now, I left it in all the time because I wasn't bothered by it). I've been on tons of things as well, including the depo shot (which I loved), and now the IUS which is perhaps the best thing ever invented, possibly better than running water. It was one of the more painful experiences of my life having it inserted, but a few days of pain once every five years, really can't complain. Anyway, the long and short of it is that you just have to keep trying to find whats right for you, there are so many options, it is a trial and error process, but once you get it right its a huge relief.
Also, you might consider going to a family planning clinic instead of your GP. I've always found the nurses at the clinics to be far more knowledgeable - after all, birth control is all they do!