In the eyes of Visa, your business must be conducted in the same region where your corporatoin exists. And, you can't process transactions for the same business in two regions.

To address your question specifically: "
If so, would it be possible for us to set it up so that our UK company processes via our US based business and receives payments in the UK to a UK bank? " The answer is "no".

I think you need to talk to an attorney.