It's a normal business expense. You account for it the same as any other goods or services.
They need to send you an invoice for you to pay. If they are VAT registered in UK, they may even be able to invoice you without VAT as it's a cross border supply.
Assuming you pay them in GBP but your business currency is CHF, you just make sure you account on your books for the currency conversion and record the expense at the CHF value it cost you to send the required GBP on the invoice.
If the CH company is using the effective VAT method, it should declare Bezugsteuer on the quarterly filing on the purchase, both input and output. It is a zero sum event.
On the other hand, if the CH company is using the simplified VAT sales method, it would declare the Bezugsteuer at the 7.7% rate and not at the simplified VAT sales rate for the CH business. Since the simplified VAT sales method does not consider input VAT, it would not be a zero sum event.