A couple of years ago, I was wondering the same on a flight to the US. A German man sat in the seat next to me and with a beaming smile said "Hello!", waved and then said "Goodbye!". That was the last I saw of him as the screen went up.
Up until then, I had tried the British approach, but I think direct and swift action tends to work best - assuming you don't want to talk to the person next to you.
I have found that if you ask "Do you mind if I put the screen up", it is often met with a "yes" and some relief that your fellow passenger doesn't have to ask the same question.
Another thing you can do is watch a Club World newbie struggle to find the button and try to lift the screen manually, but that could be considered mean