There are two unions that look after the interests of Supporting Artistes, The FAA (part of BECTU the Broadcasting Entertainment Cinematographic and Theatre Union) and Equity.
Working as a Supporting Artiste used to be a fairly closed shop and it was rare for non-union members to be offered work. Nowadays you do not have to belong to any union to work as a Supporting Artiste; however there certainly are advantages.
Unions are important because they protect your pay and your rights when you work on any production. It is their job to negotiate agreements setting out the terms and conditions of your employment, so joining one will help protect you and your earnings. Without them Artistes would be pushed into working longer and longer hours for less and less money. In addition, a union will look after your welfare, for example, helping in the event of a dispute or injury.