The website need to show on any product page two prices for example
£ 50 inc VAt for U.K mainland customers
£41.60 ex vat for rest of the world
At checkout based on delivery address the website will add vat or not. It can already do this.
The website prices will be set to be exclusive vat. Vat then gets added at checkout for u.k delivery address rather than removed for rest of the world delivery addresses.
What the site can't do is display both prices it can only show exclusive of vat if vat get added for u.k delivery addresses. This of course would lead lead to a drop in conversion rate as people don't like surprises.