Both Liberal Democrat Susan Kramer and Tory Steven Norris agree that the consequences of the Royal Parks Agency's draft proposals would be gridlock on surrounding streets.
The Agency is considering banning cars in rush-hour at four key park roads and gates, and the public will be consulted on the proposals during the summer.
Environmentalists back the plans because they say that the traffic is damaging the park and its wildlife.
Last week, the Guardian's sister paper, the Comet, asked the four main candidates their views on the issue.
Only Labour's Frank Dobson agreed that partial closure should be experimented with, and Ken Livingstone did not know anything about the issue.
Susan Kramer, who lives in Barnes, said that until there was scientific evidence showing any damage, there was no need to close the park.
Kingston council leader Councillor David Edwards said: "Not only is public opinion against closing the park, but political opinion is too. It is time for the Royal Parks Agency to call it a day."
Meanwhile Tudor Ward Councillor David Cunningham stated the case against rush-hour closure in a radio debate on London Live. He discussed the issue with a member of the Campaign Against Traffic in Richmond Park, John Repsch.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article