From what I've read (as I've never actually touched either), the Pilgrim body sits on an un-shortened VW pan/chassis so you end up with a car slightly longer than "normal".
The Chesil, OTOH, sits on a shortened pan and is the right length, but IIRC they move the headlights up 2" higher than "normal" to comply with later MOT regs. Both of them are available in left and right hand drive.
And THAT, is the extent of my vast knowledge. There are a few folks on here from Europe (Richard Maxwell - mail code de143gx - and Gerry from Scotland come to mind). If you click on the "members" tab in the black bar up above and mess around with the member search function you can see members in the UK and maybe email or PM them for more info.
I don't know if Vintage Speedsters produce a right hand drive body, or if Carey Hines at Beck does (carey@beckspeedster.com) but an email query is cheap.
Good luck!