How much did you want to overpay? Pretty sure we're allowed to do something like 10% of remaining balance per year. Which, so far at least has been fine.
And yes, this is generally how the banks work the risks I suspect. They will lose out on some deals, but gain hugely from others. For us, after 10 years of fixed payments there won't be much left (even less if kitchen appliances stop failing and giving us ways to not put money onto the mortgage)