Not sure on any time constraints on esta, would have thought that its either valid for dates of travel or not ?

Some countries require at least six months left on passports, if USA requires this then OP will be inside this time period.

Edit

For UK passport holders six month rule not applicable, passport only needs to valid for full duration of visit. No time bound requirement re passport for ESTA

OP is good to go with esta visit of less than 90 days, and that also applies to my visit, but I will be applying for a new passport soon.