An initial pair of trains between Basel and London, one each way daily, would be brilliant and I'd be confident it would be a great success.
Basel makes sense as a gateway for places right across Switzerland and perhaps beyond:
https://www.tgv-lyria.com/fr/en/booking/destinations/paris-baselLying in the far north-west of Switzerland, bordering France and Germany, Basel is the country’s third-biggest city. Basel boasts a rich historical heritage, and is packed with culture and architecture, old and new.
London to Paris - 2 hours and 17 minutes
Paris to Basel - 3 hours and 4 minutes
See the article linked to in the thread above referring to how to avoid the need to cross Paris; I suspect 6 hours could be achieved.
I passed through Basel on my Interail trip last November - struck by the separate station section (platforms upwards of no. 30) for French services that had a customs post at the entrance and were distinctly underutilised. But resetting all of this for just one
UK▸ train a day might not make economic sense, and would one train be able to make the round trip or would you need 2 sets? Interworking with shorter (Paris or Brussels?) workings?
Basel main station section
Less than fully used grand hall ...
... on the way to the rather quiet French platforms.
And onwards to other destinations ...
Basel to Zurich - 53 minutes
Basel to Bern - 58 minutes
Basel to Lucerne - 1 hours and 2 minutes
Basel to Geneva - 2 hours and 44 minutes
Basel to Milan - 4 hours and 12 minutes
Basel to Munich - 4 hours and 31 minutes