Maybe it doesn't make it any easier but your question does remind us that cataloguing and categorising people can be dangerous. I accept that there are good reasons that the state could use this information, but we should also be alert to possible abuses.
Without looking, I honestly don't know if the passport and driving licence lists this information. But the census certainly does.
I mean the issue is that British people are so uptight about the government id card when a) oyster/credit card allows somebody to track all of their movement b) there's plenty of information collection that combined can be used against you c) driving license is de facto gov id at the moment. The ship had sailed, you are fighting against the wrong thing and that's why this battle will be lost.
I might trust this government not to do that, but I don't trust a future government (because I don't know who that will be).