Launched by the Guildford Greenbelt Group (GGG) in June, the petition calls for Guildford Borough Council to return to a committee system – thus taking power out of the hands of leader Stephen Mansbridge.
So far about 1,500 signatures have been confirmed, with many more not yet compiled by organisers.
If 5% of voters sign up for it – 5,243 people in Guildford – the council will be forced to hold a referendum on changing the system.
Susan Parker, from GGG, said: “We are about a quarter of the way there and that is not including all the people who are saying to us they have a lot of signatures from Send or wherever.
“Volunteers are transcribing the names onto a spreadsheet and looking out for people from Edinburgh, for example, who are not eligible.”
So far the group has been concentrating its efforts on getting people to respond to the draft local plan consultation but will be focusing on the petition when that consultation closes on September 22.
Under advice from the council, the petition is being carried out on paper only.
“There is no deadline,” said Mrs Parker. “It is a year from the start. We will want to have enough in time for a referendum at the next election.
“It’s not actually expensive – it’s another ballot box in a room – but it’s a lot cheaper if it’s done when there is an election on.”
Campaigners, including GGG, have become frustrated that borough councillors have little say in decisions, particularly relating to planning issues, unless they are on the council executive.
“Representative democracy works better when the representative can vote, and under the executive system the councillors don’t have a voice,” said Mrs Parker.
Guildford would not be the first local authority forced to change.
In May voters backed the adoption a committee system in Flyde, Lancashire.