£4-500 would be a good safety buffer, however, you will probably need an extra 100-300 in your first few weeks for buying stuff you need, first big shop and freshers things (memberships, halls subs sometimes, trips, socialising)
£50 a week is doable but not comfortable in my opinion, it depends how you eat and live (e.g. being vegetarian or not drinking can bring cost of living down and having an expensive hobby could increase it), personally the least I've lived on is £60 a week and for me that was doable but tight (but I'm fussy about food and really hate sitting around doing little and have a lot of hobbies) but I had a separate budget for things like presents and clothes, just think on £50 a week buying your mum a £20 gift for her birthday means you're down to food money and not much else that week