Some 981 documents were submitted by 888 people to the Corporation in the first public consultation on the Heath's management. They are now being analysed by an independent research consultant.
Peter Rigby, chairman of the Corporation's Hampstead Heath management committee, said: 'I personally would not want to see this policy implemented. At this stage it is quite clear that this is also what the public want and I would have thought that the consultative and management committees will reject suggestions, put forward by environmental consultants, which envisage tree felling.'
He said it was unfortunate that the Corporation had been accused of making tree felling a fait accompli. 'We never said we would cut trees down. All we did was to put forward proposals for consultation.'
A firm of environmental consultants advising the Corporation had drawn attention to the land as it had been painted by Constable, who lived in Hampstead. In the 19th century the Heath had fewer trees, with more open grass and heathland.
Sheep were allowed to roam on the Heath until the 1930s, but the end of grazing encouraged the growth of trees. Advocates of felling say they blocked some spectacular views of London and that the closed canopy of branches destroys plants from the old ecosystem.
Many users of the Heath - including some of the most vocal and litigious people in London - were incensed by the Corporation's flirtation with the idea. One pro-tree campaigner accused the Corporation of 'botanical fascism' over the proposals.
Gay activists from the group OutRage] argued that the plans were a stealthy way of preventing men meeting each other, particularly on West Heath, a popular cruising area.
Hampstead's tree lobby has scored other notable victories in the area. In the neighbouring Kenwood estate a pressure group, Kenwood Trees, last month won a vigorous campaign against English Heritage to stop it felling trees.
The City of London Corporation took control of the Heath after the abolition of the Greater London Council.
It took over the everyday running of the area from the London Residuary Body in 1989.
Groups advising the Corporation include the Heath and Old Hampstead Society, the London Wildlife Trust and the Council for the Protection of Rural England.