OK, I wasn't going to answer as I have only had Diamorphine and thought that someone else could help better if they had experience of the two, but seen as it's you Mears!
During my first labour I was given Diamorphine, I felt more or less pushed into having it by the Midwife, all I can remember her repeating was 'we can give you little injection that will help'. I held off for a while saying that I wanted to wait until my DH arrived first. Through the blur I do remember that it was a Doctor who administered it, I had a half dose initially and it did feel good, I was giggling etc, only looking back when a Doctor came in to explain that I carried Strep B and would need an injection of Penicillin, all I could do was laugh at her and tell her that Penicillin gave me thrush on my tongue so I didn't want it (had the Penicillin in the end mind you).
Not long after I felt awful, sleepy and not in charge anymore, they gave me the second injection of it and I just felt worse, more sleepy, less in control. I wish I hadn't had it as it didn't take the pain away, just distanced myself from the pain, which was fine, but I also felt distanced from the birth experience as well.
Anyway although Diamorphine was not for me I think a Midwife should be able to administer it, afterall that surely would free the Doctor up to see to more urgent matters and although I got my injection right away I'm sure in many circumstances a woman would have to wait if there was no Doctor available.
Hope that helps and makes some sense, I haven't been getting my words out properly today.