I saw this as well. It was definitely a TV play from about 10 years ago. I also remember seeing previews for the play between programmes & this makes me think it was BBC.
The part of the soldier was played by a young Scottish actor who, I believe,was an actual amputee.
The nurse was played by a young actress who was fairly well known for her other TV appearances but I'm afraid I just can't remember who she is !
She may have been in one of the 'soaps' around this time. I remember thinking that the role of the nurse seemed to be a fairly unusual part for her to play, but that she played the part very well.
The nurse was upper Middle Class & the soldier Working Class, so as this was 1914-18 period there was a bit of a 'doomed romance' feel to the play.
The name Jed does sound familiar.
I'll keep racking my brains for the name of the actress. It'll come back to me eventually...I hope!