I assume your stipend is £10K. If so, don't forget you have to pay fees which are £3,100 p.a.? takes you down to about £7K somewhere to live will be about £3.5K, down to £3.5K which should be enough to feed you and give you a little spendng money.
Well, 13,500 will pay your tuition fees and pay for your living costs/food and give you plenty left over to live on. you shouldn't have any problem with money, it is tax-free afterall
I don't think you will have to pay any fees out of your 10 000, the fees are also covered by your grant, but they are paid directly to the university by the funding organisation ( so you in effect have nothing to do with them). And no tax or council tax. 820£ is enough to live comfortably but won't cover expensive hobbies or pay for nice holidays somewhere exotic.
Barry, the chances are that your fees will be paid for you, but not all studentships are the same. Contact the university or your new supervisor and they will tell you what is covered by your grant.