If you're not using the ID for anything official, it should be fine. If the people at the shops just look at the ID for the DOB, you should be fine, but if they scan it, you may have an issue.
With that said though, if you go down to the official place where you would get ID or your license, can't they give you a temporary form of ID that day? I know they do that here at the DMV, but I'm not sure how that would work in the UK?
Is it for a legal matter? Or just getting served or being allowed in somewhere? They normally don't check the expirary date of your passport, just your date of birth. And sometimes, because you've actually got the balls to bring out your passport and show it, they just accept that you're old enough.
With that said though, if you go down to the official place where you would get ID or your license, can't they give you a temporary form of ID that day? I know they do that here at the DMV, but I'm not sure how that would work in the UK?