"However, we are considering going on without obtaining PP as it’s very rural with only family for neighbours. "
Planning rules apply to everybody. When you go to sell, and , believe me, you will, this will bite you back big time.
And before that
Beware of enforcement and the potential consequences of having to pull the unauthorised development down.
It happens - notwithstanding some people's happy go lucky approach to legals.
When you go to re-value/ re-mortgage, there will be a BIG RED FLAG in the valuers report on the extension......................
"My question is whether a bank would offer a mortgage on a house that isn’t technically compliant with planning, and therefore rule us out of potentially remortgaging/revaluing? "
Forget the word technically - that's a nonsense. It won't be compliant. End of.
Either do it right or play fast and loose with the rules.
Your choice.
mf