Setting up Brexit UK/EU VAT pricing in admin

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I've been racking my brains trying to figure out how to actually set my site up so I can still ship to EU customers from the UK but fix pricing to fall into line with Brexit but I am at a loss on how to do it. 

Simply - I'm a UK store, charge 20% UK VAT to UK customers and show all prices in GBP inclusive of that VAT. 

As I don't have to charge UK VAT on my products if a customer is shipping to the EU because their customs will send them a customs bill I need a non intrusive way to remove VAT on EU destinations at checkout while retaining normal VAT on UK shipping addresses. 

What's the best way I can do this? 

I'll deal with notifying the EU customer they are buying VAT free but would be charged it on import etc with a notification of some sort.