The British actors' union, equivalent to the Screen Actors' Guild in America. See also Actors Equity.
An often used concept in media about the biz is that you need to be a working actor to join Equity, and you need to be an Equity member to get an acting job. The latter bit hasn't been strictly true since closed shop unions were made illegal in 1981, although it's still difficult for non-Equity members to get decent work. (The same concept also appears in media about the music industry with regard to the Musicians' Union, hence the Musicians' Guild in Soul Music.)
You will often hear references to the Equity Card, held by members, as in (with reference to later series of classic Doctor Who) "we'll let anyone with an Equity card play him".