Freelance income from different currencies (UK)

In all likelihood you will save some money by receiving the USD and CHF in your USD and CHF Revolut accounts, and then handling the conversion back to GBP yourself within Revolut.

Revolut use the real-time interbank exchange rate so you are getting a good, more transparent, rate at a given point in time.

(The only scenario when this method wouldn't be more cost effective is if the GBP happens to depreciate against USD or CHF between when you have been paid and when you convert the funds, to the extent that the GBP bank account foreign exchange fees are less than the drop in depreciation. Don't worry about this.)

Assuming that you have a Standard (free) Revolut account, note that (at time of writing) you can transfer 1,000 GBP in a given month without incurring a fee. If you need to transfer more, you need to factor in the 0.5% fee on amounts above 1,000 GBP. See fees documentation.

This has no implication with HMRC: you can specify the exchange rate used in your Self Assessment tax return.