MI5, also called Security Service is one of three British intelligence agencies. It is a security agency responsible for Counterintelligence inside the United Kingdom. Secret Intelligence Service (or MI6) is responsible for counterintelligence outside the UK, and the Government Communications Headquarters are responsible for providing Signals intellligence.
The arm of the law which works for MI5 is known informally as Special Branch. They have been rearranged as part of the Metropolitan Police's Counter Terrorism Command. MI5 staff do not have the power of arrest: what they do is instruct Special Branch, who then do the leg-work and interrogation of suspects.