Equity is the British Trades Union that represents professional entertainers. It was formed in 1930 as the British Actors' Equity Association by a London based group of actors, but since those days its reach has expanded to include virtually every conceivable branch of the British entertainment industry including theatre directors, designers, presenters (both television and radio), stunt performers, circus artists etc etc. That is everyone bar professional musicians who have their own separate union.
Its formal registered name is in fact the "British Actors Equity Association incorporating the Variety Artistes Federation", which is a bit of a mouthful. Hence it is universally known as simply "Equity". It serves much the same purpose as the American Screen Actors Guild, but the scope of its membership as noted above, is much wider.