As PP says, if you are on a 2% rate, you would be better off to find the highest savings rate that you can, there are several at 3% or over, especially if you do a fixed rate monthly saver. Save the mortgage overpayment into there and earn interest on it which gives you even more to pay off the mortgage in due course.
I am currently getting 5% on my Santander one and put away £200 a month into it.
I also repay my mortgage, I can repay up to 10% a year, and I am currently overpaying by £200 per month, and will do a lump sum in December, so I do a bit of both, but that is because I am trying to not be mortgaged til I am 67 (thanks to divorce at 40).
I have overpaid for years, and currently have 11.4 years left out of a possible 15. I rounded up the monthly payment initially to the nearest hundred, after taking payment breaks during covid, then as I earned more money, I added on another hundred.
The mortgage rate change is so annoying, I was paying £100 in interest and now it is £179 on much less mortgage than it was 5 years ago, but nothing I can do about it.
If you do overpay then you do need to check your mortgage terms allow it, and even just rounding up by a few pounds will have an impact over the years.