A key figure in the emerging Senate crossbench, Rex Patrick, has warned his party will not support the Coalition’s proposed anti-corruption body unless it is given stronger powers.

The make-up of the Senate is still being finalised, but the two Centre Alliance senators appear likely to play a critical role where Labor and the Greens oppose legislation and One Nation votes with the government.

The Centre Alliance lower and upper house members have all campaigned strongly on greater government integrity and transparency, speaking for the need to reform anti-corruption bodies, donations rules and freedom of information regimes.

Patrick told Guardian Australia that the Coalition’s flagship integrity proposal – a national integrity commission – was not sufficient.

“The Coalition’s proposed model just doesn’t cut it,” he said. “We need to have a commission which has broad jurisdiction and coercive powers to deal with allegations of corruption in the federal domain. Anything less will be viewed by the public as inadequate.”

The Coalition announced its proposed integrity commission late last year. The model was criticised for its narrow remit, lack of public hearings and inability to take public tip-offs.

Labor said it was “grossly inadequate to the task”, and the Greens are strongly opposed to any model that lacks proper resourcing, coercive powers and the ability to hold public hearings.

One of Australia’s leading integrity experts, Prof AJ Brown, believes the emerging Senate landscape could prove constructive. The two major parties are supportive of an integrity commission of some kind, as are Centre Alliance, the Greens and the returning senator Jacqui Lambie, who has previously campaigned on an anti-corruption platform.

“In some ways, it’s quite a constructive landscape,” Brown said.

“The choice for the Coalition is going to be whether they persevere with their limited – or what they would call a focused model – and not be prepared to accept amendments in the Senate, or whether they will be prepared to compromise.

“I think the landscape means that all sides should be interested in a compromise, which could potentially be a new best-practice integrity commission model for Australia.”

Pressure for an independent, broad-based anti-corruption commission has built due to a series of scandals, including the Helloworld travel saga, government water buybacks and revelations about the revolving door between lobbying and politics.

A committee of six senior retired judges who lobbied for a federal anti-corruption body prior to the election will continue its efforts to push the government for proper reform.

One of the retired judges, the former New South Wales supreme court justice Anthony Whealy, said the group will seek to meet quickly with the attorney general, Christian Porter, on the issue.

“We’ve really been trying hard to get Christian Porter to see reason and to understand that his model for an integrity commission really does have some serious defects. If they enact that legislation… then I think Australia’s international reputation is going to take a terrific beating,” Whealy said.

“Whether it’s intentional or not, the perception of it here and overseas will be that it’s an endeavour to cocoon politicians from appropriate supervision.”

Brown said the intervention of Clive Palmer in the election had helped focus the mind on integrity and finance reforms. Palmer notoriously spent an estimated $60m on a saturation advertising campaign that attacked Labor and helped prop up the Liberal vote.

“I think the really interesting thing in terms of the election, in terms of political donation and political integrity reform, the Palmer intervention has painted a pretty stark picture for people to look at campaign finance reform,” he said.