Wanting to change name after marriage, dual US/UK citizen

Hello!

New to the forum. I recently got married in the UK and am wanting to change my name on both my UK and US passports. Both passport offices have said I cannot change the passport unless the other one bears my new married name, so I'm a bit stuck, I know there have been posts about proving to the UKPO that you use your married name for all purposes and allowing a change but this only seems to apply if the other foreign passport will not allow a name change. The US one DOES but only if the UK one has been changed first...please help!

Thank you