The CRB website states this:
"Enhanced Disclosures are for posts involving a far greater degree of contact with children or vulnerable adults. In general, the type of work will involve regularly caring for, supervising, training or being in sole charge of such people. Examples include a Teacher, Scout or Guide leader".
More importantly, as far as your situation is concerned, it also says this:
"Enhanced Disclosures contain the same information as Standard Disclosures but with the addition of local police force information considered relevant by Chief Police Officer(s)".
So, it seems that it's not up to the CRB to choose which information should be included in an enhanced disclosure. If your local Chief Constable thinks that it should be included, they have no alternative other than to put it in. (i.e. if you want to get the information deleted, you'll have to write to the Chief Constable, not to the CRB).
In practice, I doubt that you've got much to worry about. I spent 15 years teaching and I knew a large number of teachers who were involved in 'minor indiscretions', such as yours. If they stopped them all from teaching, the country's education system would grind to a halt!.
Chris