Harlot there is an exemption under the DPA that says you do not have to supply a copy of a reference given, so you don't have to. It's more likely that this person could force their new employer to give them a copy though, with a few provisos. It must be stuff the employee knows already, such as factual dates and performance issues that have already been raised with them. If it's a personal opinion, the new employer should ask you first before disclosing it.
But leaving all that aside for a minute, does this volunteer know you were not happy? Just a bit strange of them to ask you to provide a reference if they know that. If he/she doesn't know, why not?
Personally I would speak to the volunteer and say you are happy to fill in a reference but your legal obligation is to be honest and give a fair reflection of the person, so you will be writing xyz and the reason is abc, are they sure they still want you to give them a reference.
As a guide, references should be fair, accurate and not give a misleading overall impression of the employee.
Referees should be very cautious about giving any subjective opinion about an individual's performance, conduct or suitability, which they cannot substantiate with factual evidence.
If you think your opinion that you wouldn't employ this person again is a fair reflection on them - ie any one else would come to the same conclusion and you have good reasons for saying that, then say it.
Your other option is to tell a white lie and say your organisational policy on references is only to provide factual information, and not complete their form but issue a letter instead just confirming dates and other factual information.
I have to say my initial thought on reading your post was why has this person asked you to give a reference, why doesn't he/she already know you wouldn't employ them again and why don't you want them to know.
You have a couple of options as I've outlined anyway, hope that helps.