Bristol desperately needs a better system of electing its city council, says a leading councillor.

Terry Cook (Lab, Avonmouth) and the rest of the council's former Labour cabinet quit last week in a row over waste treatment.

The city council is "hung", with no overall majority, and has seen a number of different regimes over the last few years.

If Labour – currently the second largest party on the council – had had a majority, it might have been in a position to ride the storm following defeat over a budget amendment.

But whichever party is in power is affected by the council being hung, leading to weaker government, says Mr Cook, who blames the situation on the election system used here.

The Liberal Democrats – the largest party on the council, but still in a minority – are now in control. They are hoping to win a majority at the local elections on June 4. But the poll will only be held in 23 of the council's 70 seats.

That's how it goes in Bristol: a third of the seats are up for grabs each year, three years out of four. In the other year (such as 2008) there is no election.

Mr Cook – who will be running Labour's election campaign – wants the whole council to be elected at the same time, every four years.

And he is launching an online campaign – with a website and a separate web address on social networking site Facebook – to see if the people of Bristol agree with him, though the idea will probably not be included in Labour's manifesto.

Mr Cook, who will be standing down at the elections to concentrate on his business as a financial services consultant, says the "all-up elections" call is a cross-party issue.

"The present system doesn't do any of the political parties any good," he told the Post. "The political leadership needs a four-year run to be able to provide stability not just to council officers but to senior personnel in partner organisations such as the health service and the police. They need to know which direction the council is going to take for the next four years.

"The problem at the moment is that for nine months of the year decisions are taken, then in the final three months there are no real decisions because people are looking over their shoulders at the next elections. For the voters, too, a four-yearly, whole-council election would be a cleaner arrangement.

"You could say to them, this is what we'll do if you vote us in for four years. If they like it, they will. If they don't, they won't. And if it's a close result, it will be clear people want us to work together."

Mr Cook has also set up an e-petition on askbristol.com which will be called 'Let all Bristol decide'. And there is a separate email address letallbristol@btinternet.com.

Mr Cook believes a change, if agreed in Bristol, could be introduced as soon as 2011.

Visitors to the websites, when set up, will also be able to say what they think of elected mayors.

Mr Cook does not personally believe there is much "appetite" for this idea, but is willing to invite a supporter of it to put their point of view on his websites.

Meanwhile, all-up elections, he believes, should appeal not only to the "chattering classes".

He told the Post: "Everyone will benefit from better government, better choice and a chance to change things."

Some members of other parties have in the past expressed similar concern about the way the present "thirds" system works.

Two years ago the Post reported that former Lord Mayor Peter Abraham believed the system was outmoded.

He said at the time: "We should have elections that fully reflect the people's wishes. At the moment they don't give the electorate what it wants."

With elections almost every year, councillors were always "in campaigning mode", he said.

He would not be drawn on what should replace the present system, although in all neighbouring authorities – South Gloucestershire, North Somerset and Bath and North-East Somerset – the entire council faces the electorate once every four years.

In many other parts of Britain, local councils continue to use the "thirds" system.