A guess: 'ackermanii' and 'Deutsche kaiserin'.

Pieter

Top one looks like Nopalxochia (now disocactus) ackermannii, and the second like Nopal. phyllanthoides.
Nice flowers there Matthew.

CP

Hmmm you might be correct with the ackermannii species. My first idea was the cultivar with that name but the species is probably a better guess when I watch that stem piece. A photo of the whole plant would help a lot here. And as Deutsche kaiserin is a selected clone from N. phyllanthoides we do agree on this one.
Pieter

Dear Pieter / CP

Many thanks for the identification. Have seen images of Deutsche Kaiserin and thats absolutely correct as the one I have.

Re ackermannii - herewith a photo of the same plant taken last year showing bit more of the plant

{{gwi:483764}}

By the way many thanks CP ! for tip regarding text editing !

Rgds
Matthew

The stem details are not too clear, but I tend to agree with CP on the botanical ackermanii. The cultivar ackermanii has mainly triangular stems with thin spines, this doesn't seem to be the case with your plant.
Pieter

It's a pleasure Matthew, glad to be able to help a fellow prickly person.

CP