Peony wilt?
Would tie in with rhubarb problems as PW is caused by one of the botrytis molds - the stuff that makes soft fruit go furry.

Cut out the affected areas and burn them.

Thank you Urbanite. I just googled it and have seen Carol Klein cutting out infected stems and also thinning the plant using secateurs wiped clean between cuts to stop the spread of infection. I now know it is necessary to burn the infected material. Thank you so much for putting me on the right track.

I'd heard that about wiping the secateurs but the spores are airborne so will be floating around as soon as you touch the stem.

I suppose it helps keep the area where you make the cut clean. Carol Klein actually threw the unwanted debris on to the lawn before gathering it up and disposing of it. It seems to have spread to other paeonia in the same part of the garden. Its disheartening but now I know what is wrong I can do something about it. I think I may need to get rid of the first affected plant.