My wife has both passports and therefore cannot get a UK ETA, so she needs to travel out using her British passport. Returning the Swiss want to see proof of eligibility so she needs her Swiss passport to return.
Is there anyway around this Catch-22?
Yes. This should always have been what she did. I show my Swiss passport to Swiss immigration (entry and exit) and my British passport to British immigration.
Edit: I also always take my British passport with me when going on holiday elsewhere and only needing the Swiss one - just incase I need to do an unexpected trip to the UK for a family emergency.
I’ve not travelled to the UK since the evisa was enforced.
Previously entry to the non-Schengen section of Zurich airport involved showing a passport. Then it would be Swiss. Before boarding another passport check was made - UK or Swiss both OK and a boarding pass stamped, even if you have it on your phone one as issued to be collected for boarding.
Now I guess Swiss passports must have some sort of evisa check at this stage too - or a UK passport.
It’s so retrograde and annoying…