To be clear, I'm a photographer. If an actor asks for headshots, I don't say 'that's £300, then invoice them £360 including VAT. I tell them straight up how much it will actually cost them.
I've never been asked to invoice a company that I definitely wasn't actually doing the work for.
Don't mean to have a go, but why?
Have you ever done a residential job where the home owner asks you to invoice their VAT registered company?