Greens of that same family are sold in the UK as collards, collard greens, spring greens, tree kale, cavolo riccio, and possibly some more names. I think spring greens taste nearest to the collard greens I had in the US.
Tesco sometimes have collard greens in their vegetable section, but kale or spring greens would be the nearest things that are widely sold I think. That dish sounds lovely! Swiss chard is similar to look at but I think it tastes different.