Yes, it's doable, although after you've bought food (and kept your budget around £25 for that, I would imagine, if you shopped wisely), it depends on how much you spend on transportation, etc. If you live within walking distance of everything you need, I can't see why you couldn't have a social life on that. You just need to be sensible. I lived on around £45-50 a week at university, although I could see my food bill going up each year because of general inflation, etc.
My housemates are stealing my food