A translation is done for business purposes if it’s done for a freelance translator in another country, and that includes one who is not registered for VAT. So if I, in Germany, do a translation for a UK client, I charge VAT only if the client is a private person.
The diagram is taken from just before section 12 of VAT Notice 741, Place of Supply of Services. There is a list of notices online, but the number is given as 742, which isn’t correct.
HM Revenue & Customs has the notices online. The reverse charge, or tax shift, is described in 15.1.
The reverse charge arises when a translator in the UK, not registered for VAT (they often aren’t, and the threshold above which you have to register is higher), does work for me. It is deemed to be done in Germany, and I have to pay VAT on it. But at the same time I can deduct this VAT payment:
15.4 How does the reverse charge work?
You simply credit your VAT account with an amount of output tax, calculated on the full value of the supply you have received, and at the same time debit your account with the input tax to which you are entitled, in accordance with the normal rules. The partial exemption implications for reverse charge services are explained in Notice 706 Partial exemption.
The relevant parts of the statutes are mentioned in these articles or in the VAT notice.
Article in English by Kay Fisher at Translatorscafe.