Camden council is having to cut spending by pounds 28m and has had to appeal to the private sector to finance the fence in Lincoln's Inn Fields, Holborn.
The plan is to stop the square becoming an encampment again after alternative accommodation has been found for the homeless people who have lived there for years.
The council has decided to ask the Lincoln's Inn Fields Association and other local organisations, which have been pressing for the homeless people to be removed, for contributions towards the cost of the fence.
Aiden Padden, a spokesman for the council, said: 'We are in the situation of having to save pounds 28m across all departments in the rest of this financial year and the whole of the next.
'We certainly would hope for support from these organisations and preferably would like them to pay for the entire cost of fencing the square off.'
The presence of the down and outs in the centre of one of London's finest squares has been a source of controversy among the well-heeled lawyers and businessmen who have offices there.
They and local residents claim that they have been threatened and sometimes attacked, that thefts have been rife and windows broken. The inhabitants of the makeshift encampment in the square have been blamed.
The Lincoln's Inn Fields Association has been demanding that Camden council should enforce park by-laws which forbid camping, and has threatened to take legal action to ensure that this is done. But now the council has put the ball back in the association's court. Philip Hawkins, head of the leisure services department, said he would be canvassing local organisations to assess support.
Camden's policy is that proper alternative accommodation should be provided for the square's unofficial inhabitants before they are moved out. The Government has appointed a task force to achieve this as part of its initiative on people who are sleeping rough.
It is hoped that this can be organised by early next year, but the centre of the square will then have to be fenced off to stop a new influx of homeless people. Camden believes that this will cost about pounds 65,000.
Mr Hawkins said: 'It would enable the gates to be locked and unlocked on a daily basis and represent a more permanent solution to the difficulties at the Fields.'
Richard Griffiths, chairman of the Lincoln's Inn Fields Association, said that it had not yet received the request for financial backing from the council but that it would be considered sympathetically.
'We would do whatever we could as a group to help if sensible proposals were conveyed to us by Camden. However, we do not have any funds at the moment.
'It is one possible course of action, when the other problems of the Fields have been dealt with, that there should be a railing.'
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