As Ubasses states, banks need to get people to save with them if they're to have any money to lend out (and to make a profit from). Halifax has recently been applauded by many people for increasing their savings rates:
http://www.telegraph.co.uk/finance/personalfinance/savings/10168951/Is-Halifax-0.45pc-rise-a-sign-of-a-savings-rate-turnaround.html
Once unemployment levels fall to below 7% the Bank of England will inevitably increase the base rate. Any initial changes are likely to be fairly small (e.g. from 0.5% to 0.75%) but they will almost certainly gradually creep up to more sustainable levels, such as 3% or 4%. (If Mark Carney and whichever Chancellor is in Downing Street get it wrong, and we end up with high inflation, the base rate could exceed to 17% record set in 1979). So anyone with a mortgage needs to be budgeting for
substantial increases in their repayments over the coming years but savers will, at last, seem some reasonable returns upon their investments.