That should be pretty comfortable. I got 8k from the AHRC this year for my MA and, whilst living with my fiancé has reduced some costs, I had more than enough to get by. If I hadn't bought a lot of new things (pc, tv, games, sky, antique books, etc) then I'd probably have a fair bit saved up now.
A lot of things depend on your accommodation; we pay £550 pm between us for a 1 bed flat in Manchester, and the electric/gas bill seems to hover between £40 and £80 pm, food I'm not so certain of. Unless you live on lobsters and caviare, with 13k you should be able to live comfortably and have enough spare cash for a few luxuries.