The Alkathene I have come across in 1/2" has about a 15mm bore and 3/4" (not quite 22mm) external, by I don't know what class that would make it. It is quite common to connect to the type of pipe I've come across by shoving a bit of 15mm copper tube into the bore and using a 3/4" compression fitting (i.e. using a 22mm fitting with an imperial olive and a fair bit of PTFE). May be worth more detailed photos as it sounds like Exedon2 might have an inexpensive solution.
I suppose if you wanted a slightly more expensive solution that wouldn't require too much of the kind of black arts myself and Shaun seem to be considering and wanted to get rid of the redundant stopcock (which would be a good thing to do), then Philmac universal fitting onto the black pipe and connect to modern copper tube from whence it is easy to make connections to your new stopcock.