I know what you mean John but "almost impossible" to me just poses a challenge!
Surely it can't beyond the wit of (UK) man to make this happen, even given the constraints of each country. I agree that the receiver is likely to be the main problem (especially if you are considering parts kits in the US which have everything but that for obvious reasons) but when you think about it there is limited overlap with the various jurisdictions. Apart from the need for a new un-ported barrel in the UK and the question of the receiver and bolt/carrier, all other parts needed for a straight pull should be unrestricted over here.
I agree it's never going to be quite as per the original, but given the constraints here and in North America nothing ever will be. But that doesn't stop us all striving to get as near as dammit if we can.
I acquired an HK .22 kit for the C1 from Canadanot too long ago which I imported in the most straightforward way on the permissions granted by my firearms certificate. The interesting thing was that when applying for the export paperwork the seller in Canada was challenged by his local customs office as to why he was wanting to ship a kit for a firearm that was prohibited in Canada. I provided a suitable reply (along the lines that .22 semi autos aren't restricted in the UK) and lo and behold it arrived in the UK shortly thereafter. Motto of the story - there's always a way!
If you manage to make some real progress with your C1 project and need some handguards let me know - better that there's at least one complete one in the UK than two collections of parts!
Cheers, Kev