The obvious answer is if the net interest paid by the bank is higher than the mortgage rate, then stick it in the bank.
Although the temptation would be to pay a chunk off the mortgage, you can do that at anytime with the money in the bank account, as long as it's not tied up .... so if in the future you find yourself in a position where the mortgage rate is higher than the savings rate, you can withdraw the money pay a chunk off the mortgage, but remember to keep some back for emergencies, etc.
In my opinion, interest rates are only going to rise in the near future and seeing how you're fixed at 2% for the next 10 years, I personally would just pile all my spare cash into a savings account, as long as it pays over 2% net ..... but be wary of tying it up for too long, in case things change suddenly.