Mr Watson alleged that a member of the group had bragged about links with a senior aide to a former prime minister.
Commander Peter Spindler from the Metropolitan Police said: "This is a complex multi-agency investigation supported by the NSPCC, Ceop and Richmond Social Services involving non-recent allegations of sexual assault against children.
"It is vital that anyone who has been affected by or has information about activity in the early 1980s at the Elm Guest House, or the Grafton Close care home in Barnes, speaks to the NSPCC on their helpline on 0808 800 5000, or their local police."
A spokesman for Richmond Council, which ran the care home, said: "Richmond Council considers the safeguarding of all children and young people as an utmost priority and we take any allegations of abuse very seriously.
"As such we are offering our full support and co-operation to the police during their investigation. As the investigation is ongoing, it would be inappropriate to comment further at this time."