Luckily I have a second British passport with an exactly 10 year life and this was accepted by ESTA instantaneously. Fortunate as I'm travelling to JFK on Monday (although I accept that the system is not yet mandatory).
I wonder if my other passport's 10 year and 9 month life (exactly) is just a Passport Office error as I'm sure the max life of a passport is 10 years in the UK?