If you can tell us whether or not you need to be able to access the money or keep it out of reach, if you have an opening balance, are comfortable with internet banking etc etc. then you might get a valuable answer.
Incidentally, if you have a deposit and favourable results on a credit search (which this savings account may have little or no impact on) then you'll get your mortgage. I fear that (other than the amount saved) your savings will have little impact as far as the loyalty/history goes.
I think moneyfacts.co.uk or .com give info on lots of savings accounts. ISAs can effectively be tax free equivalents of simple savings accounts so they may be a place to start as they'll pay a higher rate of interest (cash-mini ISAs that is). Remember that any interest rates quotes are before tax is deducted unless it's an ISA.