A council claims it will "struggle enormously" after receiving just 10% of the grant it applied for ahead of the Olympics.
The Greater London Authority is handing out grants to London boroughs to cover the cost of the Games.
Camden Council got £200,000, despite asking for £2m. Meanwhile Merton Council got 140% of its requested £500,000.
The Mayor of London said discussions with the council were ongoing.
Councillor Tulip Siddiq, cabinet member for culture at the Labour-run authority, said: "This is a very poor deal for Camden.
"We're going to struggle enormously with limited resources.
"How can we be expected to find more than £1m to provide for the Olympics?"
Camden, which is not one of the boroughs where Olympic events are being staged, claims to need the cash for street cleaning and to crack down on illegal street traders.
Camden Town lies about 11 miles from the Olympic home borough of Newham.
A spokeswoman for Boris Johnson said: "The mayor and the GLA continue to have constructive discussions with Camden.
"As the borough knows we plan to get back to them in the next month."