Does it work with Xero, QuickBooks or FreeAgent?

Yes. Open Business details, find Connected apps and press the plus beside Accounting. Choose Xero, QuickBooks or FreeAgent and sign in there.

From then on, every invoice you send goes across on its own, with its customer, its lines and its VAT. Edit one and it's updated there. Delete one and it's voided there.

Payments don't go across. Your bank feed brings them into your books, and sending them too would count them twice.