I think you're confusing yourself. Just decline dynamic currency conversion and take out the money in GBP. Any ATM in the UK that says free cash withdrawals (being the vast majority, including at LHR) will be just that - free.

ETA: The Link website https://www.link.co.uk/consumers/locator/ has a comprehensive list by free/chargeable. I thought all the Travelex ones at LHR were free but seems some now charge £2.50. In any case, no way you should be paying currency conversion.

Your bank may well of course charge fees on their end, but those are not imposed by the ATM.

If the ATM itself says they are charging a fee for GBP, just cancel and find one that doesn't.

Incidentally, you really don't need cash at all in the UK*. In fact in London it is actually quite hard to spend it. But each to their own.

*certain establishments in Hounslow may be an exception, but that's really increasingly rare