Yes, I have gone through this process very recently with a large bank beginning with L. It was only a small remortgage, building insurance was mandatory, life insurance and critical illness insurance were not. The mortgage advisor asked how I would deal with each of these eventualities, I have sufficient capital elsewhere so no problems.
I did not mention PC at all, it is none of the lenders business and would be discriminatory to ask. It would of course be an insurer's business, but as said that was irrelevant for me.
I know the lender has the house as collateral, but they want to know how it would be paid off in an emergency, as they are not keen to be seen to throw a widow and children on the streets. As long as you have a credible and true answer to that they had no problem.
Of course other lenders may have different policies.