If you look at Lloyd’s under the actual documents accepted they don’t list it there.
They even state that: “The Biometric Residence Permit card may not be accepted in all our online journeys. You may need to provide additional documentation.”
Both HSBC and Barclays don’t accept them, not even to pick up a card from a branch.
EU identity cards are accepted but UK BRP and BRCs aren’t https://noidnosale.com/acceptable-forms-of-id-in-the-uk
If you managed to use yours for anything other than border control then it’s because whoever inspected it didn’t knew the rules.