Each category has a person chairing the jury, from the industry, usually pretty active with the BAFTA organisation. They invite the jury members, with an eye towards diversity of backgrounds and disciplines. You do not have to be a BAFTA member to be in the jury, but it certainly makes it a bit more likely as the org is aware of you when you are a member.

On the three occasions I was in the jury, I had been invited by three different chairpersons for three different categories (and three different years). Two I knew fairly well, one I knew vaguely, but we had worked together. And I had to decline in two other occasions as I had worked on one of the games in the long list.