I live in London and I'm a student. I've been fortunate enough to have parents that are totally on board with veganism and healthy eating so in that respect my life is simplified. The suggestions everyone has given are excellent!
I also keep a money box and throw in my change. Then at the end of the month I count it up and buy an ingredient I like - something that's a treat. This month it was match green tea powder, last month it was vegan marshmallows. You're doing a good thing so keep your chin up xxxx
how about trying trader joes? Their food is awesome and VERY reasonably priced- PLUS they have frozen dinners etc, but they are WAY more healthy than the normal tv dinners in the regular grocery store. Fruits, veggies, whole grains, root vegetables etc are all MUCH cheaper at T-joes and most of their stuff is organic as well:) Check em out- www.traderjoes.com:)
You really need to talk to your parents. I know that's probably not what you want to hear, but it's impossible to be secretly vegan. I mean, even if you managed to find a way to eat enough, at some point your parents are going to notice you're eating differently and be concerned, right?
You say that they won't understand or be supportive, but you can help them to understand. Start with this article: http://www.thisdishisvegetarian.com/2012/09/help-my-kids-gone-vegan-guide-for-non.html or some of the resources that it links to. Talk to your parents about WHY this is important to you, and let them know that you've been going hungry instead of eating things you don't feel you should eat. If they're worried about the cost of vegan foods, go to the library or one of the paperbook swap websites and get a copy of Eat Vegan on $4 a Day. It's possible that with their support, your going vegan could save them money. Give them a chance to understand - no one can until we explain it to them!
You simply can't starve yourself. You're still a growing young woman and you need proper food or you will become ill.