The answer depends on what else you'd do with that 2%. But first, let's look at some actual numbers.
For simplicity's sake, let's say you have a £100k mortgage outstanding, your payment is £1000 per month, and you want to pay £1000 extra per month. 2% interest, compounded monthly for simplicity, so .02/12 = .00167% per month. (Your interest is probably compounded daily, but this simplifies the math and isn't too far off of it.)
If you don't pay it off early, then first month, you'll owe £100167, minus £1000, so £99167. Second month, £99332 after interest, then £98332 after payment. So on and so forth. After 24th month (2 years), you'll owe £79613 after that 24th payment. So you've paid off £20,000 of balance, at the cost of £24,000; total interest paid, £3,613.
If you do pay off another £1000, so you put a total of £2000 in per month, which is penalized (.02*1000=£20) each payment, for a total of £48,000 paid over the 24 months. After that 24 months, you have a balance of £55,637, so a bit over £44k paid off, at the cost of £48k; total interest and fees paid, £3,637.
So, at the end of the 24 month period, you've paid an extra £24 in interest/fees than you would have otherwise. You of course have a lower loan balance at the end, but you haven't saved any money overall, and if you're just refinancing at this point into a new loan, you're no better off (and very slightly worse off), even assuming the money will just sit in your bank account and do nothing. I think with daily compounding interest it will be around the same or slightly better, but it's not a significant amount.
Now, there is a third option, perhaps: pay £24000 (so after penalty, £23,520) on the first month. This is that whole extra £1000 per month, all up front, where it makes the most difference for interest.
This does help, some: you pay £3,172 in interest, around £450 less. Sounds good to me, right? Except, you might be able to make more than £450 with that £24,000. £450 is 1.875% of £24,000, meaning you just need to make a 2% return on your money to beat out this option (and in fact, that's not surprising, given the 2% interest rate!). Investing in the market, even conservatively, is likely, though not guaranteed, to be beneficial; over a 2 year period it's fairly risky, though if you can think over 5-10 years, it's very likely to be substantially better. Even a 4-5% return (well below long-term market averages) will be quite a bit better, and the market's down quite a bit right now - so it might be even better than that - though it's still a risk.
You can make a term deposit (looks like "Fixed rate bond" is the term), even, and at least break even - right now it looks like 1.9% is common for a 2 year term deposit in the UK.
In total - my recommendation would be against paying off the mortgage early, particularly in this 2% interest rate period. 2% is around inflation levels, meaning you're not really paying any real interest, from one point of view. Once the rates are higher (4%+) then it may be worth considering.
The exception here - basically the standard exception to these questions - is if you are otherwise going to spend the money on luxuries. In that case, you're better off prepaying the mortgage, at least from a personal finance perspective, if you can do so up front - but not if you're going to do it monthly. What is better for you personally in this regard is a question only you can answer, of course.