The country to which the ba.com site is set does not matter for these purposes. The key is where the ticket is issued. If you buy a straight cash ticket on ba.com, by default it is issued in the country in which travel originates. In order to MFU, the ticket must be issued in your BAEC home country. So if you try to do something clever, you can accidentally cause a mismatch that prevents you from MFUing.

If you book a PAR-LON-SIN-LON-PAR itinerary on ba.com, buying a straight cash ticket, you should get a ticket issued in Paris. Once the ticket has been issued in Paris, no sector of that ticket can be upgraded using miles from a UK-based BAEC account.

If this is what you want to do, you must either book and MFU simultaneously during the booking process (ie not upgrading after booking) on ba.com, or do the whole transaction by phone call to the UK service centre.

However, if you book an itinerary starting in the UK, you will by default get a ticket issued in the UK, so it then matters less whether you book and MFU simultaneously during the booking process), or book the cash ticket first and then MFU via MMB on ba.com (or on the phone).