First some simple facts have to be understood. The UK government requires that you make payment of your tax in pounds sterling. Nothing else will do.
Well, no, not really:
Q. Which tax and National Insurance liabilities can I pay in euro?
A. You can pay any tax or National Insurance liability in euro, and we will convert the payments into sterling.
You can pay by:
Bacs Direct Credit, Internet or Telephone banking
Euro denominated cheque
Euro notes (HMRC offices at Ports and Airports only)
You can find further details about euro payment procedures in the area specific guides within the Paying HMRC section of this website.
The rest of the theory rather falls down at that point.