In the UK, is it possible to get a memorandum of a caution? when no conviction was actually made?

According to what Gary's been told, no, not in his case. He contacted the police branch where his caution offense occurred, and they (eventually) told him to submit a request at his local station, asking for any and all records of his arrest. They said it was doubtful they'd have anything beyond the basic information on his subject access report because his caution was issued more than two years ago and they don't keep the records beyond that.

It's worth a shot to try to get any additional information you can, though, especially if the caution is of more recent date. The police are baffled by why Gary would need or want information about a simple caution, and they've given him a bit of a runaround about it, like it isn't worth their while to try to dig up some info for him. They keep trying to give him his subject access report again, and he keeps having to explain that he already has that.

He's going into his local station today to see if they can do anything about digging up records.

I just talked to Gary. The local station was somewhat more helpful. They told him to call the local branch where his caution was issued and request information regarding the incident from the EAB or "Evidence and Actions Book". They are supposed to keep this book for seven years, but he was warned it may have been sent to "Central". It wasn't clear whether or not he'd be able to get any info if the EAB had already been sent on.

Hope this helps.