PMB
It might be worthwhile phoning Sarah at Brands Hatch Morgan. They have many continental customers as they are in Kent and she might know if they have any problems getting to the UK.
I took a van to Switzerland a few years ago and the only check was at the tunnel getting back in to Britain.
As Switzerland is in the Schengen Agreement there were no checks at any other borders.
If you leave Switzerland via Basel you can save a fortune on french tolls by travelling via Luxembourg and Belgium. I reckon I save €50 each way and that’s without a trailer.