I'm wondering if you would be able to get a new sim card with a monthly 'roll-on' contract (ie just needing 1 month's notice when you wish to terminate your contract).
You would need to pay by Direct Debit each month and so might need a UK bank account but you would get minutes, texts and Data allowance within the cost of the monthly fee. So, depending on how much you will need to use the mobile - probably quite a lot.
Maybe someone else will be able to give you a better idea.
A PAYG sim is probably cheaper online but the phone shops will sell them too, I would think.