I've never been 'invited'. It's unlikely to happen either because of reasons.
I'm only responding because I've just remembered getting a first for my essay on the jury system. I was the only person in my year to argue against it. I decided to argue against it for the hell/novelty of it, but as it went on and as I did more research I genuinely came to the view that there is as much against our jury system as there is for it, and possibly a little more (against).
The two main issues I recall I had were:
1. a lot of people are precluded from jury service, and then a whole bunch more can be excused from jury service, so what's left is those people the state approves of, and who can't get out of it. Not necessarily good or representative.
2. juries sometimes have an agenda. There are cases where juries have been clearly directed by a judge that because of a or b the jury must reach a particular verdict or must ignore such a piece of evidence. And then the jury does the opposite. Whether you think that's right or wrong, it isn't the law.
Since then the number of cases that can be tried without juries has increased massively. I wonder now whether the jury system is merely a token gesture: something to be referred to by one party or another but which is largely meaningless.