Hey there, I am in the same situation as you, I phoned Jobcentre as well like 4 weeks ago and they told me that the StudentFinance will sort this out. After a two weeks or so I received a letter from Jobcentre to register for a National Insurance Number. I am still waiting for the NI to arrive tho, so I can pass it to StudentLoan. I phoned also the StudentLoan and they told me as soon as you receive your NI, then just call us and we will put it in the system, which will take another 2 weeks to process ¬.¬ You should get your grant though.
By the way, if you think you are not able to pay the Tution Fee at time, then just call your University up and explain to them your situation, as they can borrow you the money till you can pay and with no interest-fee. Qoute me for further sex-instructions.