I'd use Customer Groups to handle this. Just set the product up in the normal way with a tax class of "Taxable Goods".
If the customer is in a certain customer group then they don't get charged VAT, otherwise they do. How you handle sorting customers into groups is up to you, you could just add a checkbox to the signup form to determine which group a customer should be in.
To set up the Tax classes
In Sales > Tax > Customer Tax Classes add a new group e.g. Ex VAT Customers.
In Sales > Tax > Manage Tax Zones and Rates create a new rate called TAX Exempt at 0%, you'll probably want to select the UK as well. You'll probably already have a UK rate set at 20%.
Then in Sales > Tax > Manage Tax Rules create a new rule selecting the following
- Customer Tax Class = Ex VAT Customers (or whatever you called it above)
- Product Tax Class = Taxable Goods
- Tax Rate = Tax Exempt (created above)
Assigning tax rate to Customer Groups
In Customers > Customer Groups create a new custom group and assign the new tax class from above (Ex VAT Customers).
Now whenever a customer in that group places a "Taxable Goods" item into their cart there will be no tax charged.
Limited to certain products?
If this is limited to only certain products then you'll have to create a new tax class and assign those products to it rather than to the "Taxable Goods" class. Also, when creating the rule above, change "Taxable Goods" to whatever you call the new rate new tax rate.