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Ok... I have a bit more info now - from an accountant who does work Saturdays!
Apparently, if I set up a separate company - either partnership or sole trader, which has nothing to do with my existing company, I can charge no VAT, BUT if the VAT office suspect any link with the existing company, they can insist it is still part of the VAT registered company. The Accountant is checking those 'links' now, but it could even be as small a link as trading address, phone number, name of Director/Partner... The VAT office don't like people having multiple companies... Might be the easiest option just to do it through the existing company and pay the VAT - which means charging more money!