Should I overpay my mortgage if I plan on going into rented accommodation

You are better off overpaying if your mortgage rate is higher than the savings rate you could get with that money.
Only other consideration is what savings you have, you should have a good buffer for unexpected events, so if say that's £10k, put that aside and only then cosidr overpayment if the interest rate calculations say so.

No, that is not paying interest.

If you save the 1k you will earn interest on that 1k AND have paid interest on the equivalent 1k on your mortgage. For each 1k you pay off your mortgage you don't pay interest on that 1k, but you also forgo the interest you could earn.

AnotherJoe has described it perfectly.

SammyS1987 wrote: »

Thanks Steve, that helps.

So the £1000 overpayment in effect buys me £1000 of the house back from the bank which I then don't have to pay interest on, and if I sell the house that £1000 chunk of equity is mine to sell rather than theirs so I keep the money?

Spot on. Let's say you pay off £1000. At (say) 3% mortgage rate then next year that's saved you £30 that year and each subsequent year. If instead you had that £1000 in an account paying you 1% you'd only earn £10 (and perhaps pay tax on it) so you are at least £20 better off each year.

And then when you sell the house, you owe £1000 less so you get back £1000 extra when you sell it. It's effectively banking it, but in your house instead of a savings account.

Obviously the numbers I've used are relatively trivial amounts and only make a big difference over long time periods and larger amounts. For two years, unless you are paying off tens of thousands, there may be a benefit to losing out on a small amounts of gain for the benefit of having some spare cash around rather than being locked up in your house.

So it all depends on how much, how long, and interest rates.