Mr Morgan, a 37-year-old father-of-two, was killed with an axe in the car park of the Golden Lion pub in Sydenham, south-east London, in March 1987.
A string of inquiries over the decades unearthed allegations of corruption.
The 2021 report said police officers’ membership of the Freemasons had been “a source of recurring suspicion and mistrust in the investigations”.
The Met’s decision follows a survey of officers and staff which showed two thirds of respondents felt membership of such organisations affected perception of police impartiality and public trust, the force said.