The Friends of Richmond Park has also said that a planned modernisation of the UK’s airspace threatens the “world famous green space”.
Last week, two proposals were submitted for a new runway to be built at Heathrow airport, which could be operational by 2035.
Heathrow has said that its plans, which would see a new 3,500-metre runway open to the north-west of its existing location, would increase the number of flights per year from 480,000 today to 756,000.
It comes amid efforts by the government to modernise flight paths across the UK for the first time since the 1960s.
A spokesperson for Heathrow airport has said that the airspace modernisation programme aims to “improve journeys and reduce emissions and noise impacts”.
But the Friends of Richmond Park have claimed that new flight paths and a third runway at the west London hub could be “catastrophic” for the park.
Chairman Roger Hillyer said: “The proposed reorganisation of flight paths and extra flights resulting from the expansion of the third runway could cause severe damage to a world famous green space, the quietest and most protected park in London, cherished and visited by all Londoners, not just those who live around it, and one of the richest areas for wildlife in the country, changing it forever.
“We believe doing the minimum to change existing flight paths is a viable alternative that allows Heathrow to make best use of new aerospace technologies, grow its business and meet its net zero commitments on climate change.”
Heathrow has said that the process of changing flight paths is in its “early stages” and that final decisions are “yet to be made”.
Transport Secretary Heidi Alexander said: “I am pleased to have received the initial Heathrow expansion proposals – a significant step towards unlocking growth, creating jobs, and delivering vital national infrastructure.
“We’ll consider the proposals carefully over the summer so that we can begin a review of the Airports National Policy Statement later this year.”