It's also worth talking to your current bank in Switzerland. Maybe they can offer some sort of solution, given the faff that would be involved in setting up a bank a/c in the UK. At least they would be able to provide a credit / identity reference.
You could also persuade your client to pay in a different way. As long as you have an IBAN number, they should be able to pay directly into your Swiss account (you will have to cover the exchange fees).
Many years ago, I had a client in France who insisted that I have a Euro-denominated account before they would pay me. I went to some considerable lengths to open one (my branch staff didn't even know Barclays have such a thing), only for the cheque to arrive in £ sterling.