Now that I have more time, I can give you a fuller answer

If you booked your redemption through the Avios Travel Reward programme, you can upgrade the class of travel in the same way as if it was booked through the Executive Club so it is not absolutely necessary to move your Avios from one account to another to do this. Same applies if you booked through IB Plus. There will be a admin fee - £35 if memory serves plus any uplift in Avios/taxes/carrier charges.

If this gets you nowhere, it may be possible to upgrade each flight at the airport with cash. Upgrade offers are not guaranteed though. If you visit the http://www.flyertalk.com/forum/briti...ng-thread.html, it will give you an indication of cost.