The Electoral Commission has alerted the Met about "potential fraudulent registration of voters" in Tower Hamlets.
There will also be elections for directly elected mayors in Hackney, Lewisham, Newham and Tower Hamlets.
Mr Livingstone was visiting Greenwich, Tower Hamlets and Southwark to discuss crime and policing.
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The charity claimed the ownership did not automatically transfer to Tower Hamlets Council in east London.
BBC: Henry Moore sculpture sale faces Art Fund legal challenge
By contrast, Tower Hamlets pays the entirety of care costs even for people with such savings.
Allegations of postal vote fraud in Tower Hamlets were also made to the Electoral Commission in 2010.
Tower Hamlets said it will do everything possible to improve its recycling with or without government intervention.
BBC: NEWS | UK | England | London | Council faces recycling hit squad
The nine boroughs being targeted are Brent, Camden, Hackney, Haringey, Islington, Lambeth, Southwark, Tower Hamlets and Westminster.
Mr Justice Males concluded Tower Hamlets council's payment policies were discriminatory, following a High Court hearing last month.
Tower Hamlets is home to London's second financial centre, Canary Wharf, which paid for half the council's bid.
The Electoral Commission called in Scotland Yard after allegations of postal vote scams in Tower Hamlets last year.
Tower Hamlets, which currently has 11, wants to be the first council in London to ban the practice altogether.
Tower Hamlets disputed her claim and said it was "not alone" in making additional payments to unrelated foster carers.
It said Scotland Yard needed to review its plans for policing the next elections in Tower Hamlets in 2014.
Such is the concern about Tower Hamlets's performance on recycling that the government is considering intervening to improve things.
BBC: NEWS | UK | England | London | Council faces recycling hit squad
Stephen Deuchar, director of the Art Fund, said following Bromley Council's claim "Tower Hamlets's cavalier plans" must be halted.
BBC: Bromley Council disputes Henry Moore sculpture ownership
This national average included wide regional variations - from 47.5% of primary pupils in Tower Hamlets to 4.2% in Wokingham.
The other side of the counter, Lee Brown, 30, has been taking bets in Tower Hamlets for the past year.
Tower Hamlets, the borough that now contains Spitalfields, plays host to the largest community of Bangladeshis outside their native country.
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However, the Tower Hamlets borough council issued a statement on Thursday describing the Art Fund's move as a "desperate PR stunt".
BBC: Henry Moore sculpture sale faces Art Fund legal challenge
However, Councillor Rania Khan, Tower Hamlets' cabinet member for culture said they were being "judged rather harshly by the art world".
The counselling scheme is being piloted in Wythenshawe and also in Tower Hamlets, London, Harlow and Northumberland over the next two years.
But in Tower Hamlets a decision has been made to treat all of Banksy's stencilled artwork as graffiti to be painted over.
The Tower Hamlets Federation of Tenants and Residents Associations told the BBC the council's decision was "understandable given the current economic climate".
And Tower Hamlets is the perfect environment for a smoking culture born of deprivation to flourish, Mr Brown tells me between punters.
In Kensington and Chelsea it is 8.3% and in Tower Hamlets 8.1%.
Tower Hamlets LibDem Councillor Stephanie Eaton said it made more financial sense to spend money on recycling facilities than on land fill tax.
BBC: NEWS | UK | England | London | Council faces recycling hit squad
"Tower Hamlets has a dire shortage of affordable housing with over 22, 000 on the waiting list and considerable over-crowding issues, " its spokesman said.
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