Personally I would suggest you use your passport as ID
Best practice is to keep things as simple as possible.
When you apply for the FLR(M) you'll need to enter your name as it appears in your passport anyway.

Your marriage certificate is your 'audit trail' document from maiden name to married name.

In England you are quite free to use whatever name. UKVI will always want to reference the name on your passport.

Many folks don't update their passport to married name until it's time for renewal. No problems at all.

Good luck