When do mortgage payments go down?

Horizon81

So say you overpay by the maximum amount allowed per month (20% on a £400/month repayment would be £480) Does the monthly repayment (before overpayment) reduce? E.g. the £400 a month reduces to £398 a month + the £80 overpayment = £478 a month, then £476 the month after as each months overpayment chips away at the capital (I realise these figures aren't exact, just for the purposes of the question)

The alternative as I see it is to keep the payments the same each month (£480) and reduce the term, but the term would reduce with every month that passes. I read in another post that the lender would need to write to you each time the term changes to agree the new contract, but this would get tiresome each month!