Spurr said: "The Royal Parks will not agree to the removal of any trees or the pruning of mature branches. The only pruning that will be done will be of small, feathery branches, in five areas of the park."
He also said a section of the park would be closed "for some weeks" to prepare for the event but it would only be fully closed for three days around the event.
Pressure group NOGOE (No to Greenwich Olympic Equestrian Events) claims the "whole park will be closed during the actual Games (29 July to 10 August 2012) and the Paralympics (31 August to 4 September 2012)".
Spurr has been listening to local protests for the past year, but he said local relations have been improved by greater communication by London 2012 organiser the London Organising Committee of the Olympic Games (LOCOG), which held a roadshow in the park last weekend.
"It was well attended," said Spurr, "and there was a mix of those who want it and those against it.
"But some who were strongly 'anti' went away feeling it was actually well worth doing once they heard that what has been written about the situation was not accurate."
Journalist Andrew Gilligan has been campaigning against the equestrian event taking place in Greenwich Park, claiming London Mayor Boris Johnson "has been misled into backing (the) controversial plans".
Spurr is spending two days a week planning for the event in 2012, meeting regularly with representatives from LOCOG - including recently appointed course designer Tim Hadaway - to finalise the course route.
"We're having detailed discussions about rootzones - so we can protect the trees or avoid affecting them. While the route will go through the flower garden it will no longer go through the lake, and the main disruption will be to two small circular beds, which will not be planted with bedding that summer," Spurr said.
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