Alternative - overpay your mortgage payments now, and if you've just got 3 years left, there's a good chance it can be paid off by the time your fixed rate ends.
Top of my head, average fixed rate is around the 3% range, and you're right, you would be hard pushed to find a savings rate to match this.
Then again, I imagine the interest on the balance is going to by now be peanuts, nevertheless, it's peanuts better in your pocket (And even if it's just over a pound, that will buy you some peanut butter to dunk a banana in)
It's a nice feeling that you have little to pay on such as your mortgage I imagine. Now I am no expert, but I do keep in touch with the financial predictions (I have to). Most "experts" are not expecting anything to happen to the interest rates in the short term, and some even are predicting it will stay very low for a matter of years........perhaps even those two years (But I really wouldn't bet on it).