The Greens have commissioned novel legislation aiming to establish a parliamentary commission of inquiry into the big four banks following years of complaints about hidden fees and charges, credit card gouging, alleged collusion over interest rates, dishonoured insurance policies and squandered life savings.

The plan, presented as a potential game-changer, involves creating the parliamentary equivalent of a royal commission using similar terms of reference and structure, the appointment of a three-judge panel, identical powers to compel witnesses but reporting to the Parliament rather than the government.

It is a form of inquiry used only once before in Australia.

With the legislation drafted, key crossbenchers are said to be favourably disposed if not yet formally onside.

Pauline Hanson's One Nation is thought likely to support.

​Other independents in the lower house are also likely to support the idea, including the renegade Queenslander Bob Katter, Andrew Wilkie (independent, Tasmania) Rebekha Sharkie (Nick Xenophon Team) Cathy McGowan (independent Victoria).

​The proposal will put particular pressure on the outspoken LNP MP George Christensen and his New South Wales party room colleague Senator John "Wacka" Williams. Both men are unabashed critics of the banks and have signalled their intention to support a royal commission.

In recent days, Mr Christensen, an arch-conservative regarded as the Coalition MP most likely to break away from the Turnbull government should it stray from its conservative mission, has come under renewed scrutiny.

He has indicated he would cross the floor in the House of Representatives but only to support genuine action, rather than merely a resolution designed to grandstand.

On Friday, Mr Christensen used to Twitter to clarify his position on floor crossing: "I won't vote 4 pointless motions re banking royal commission as they deliver nothing but a political attack on the govt. Will only vote 4 bill".

This proposal appears to satisfy that concern.

The Greens intend to release an exposure draft of the enabling legislation on Tuesday.

However to succeed the new inquiry would need Labor's backing and all of the lower house crossbenchers plus Mr Christensen and at least one other government MP.

Greens Treasury spokesman Peter Whish-Wilson, a former banker, said the approach had been conceived as a way to break the impasse.

"If the will is there, this is a way forward," he said. "This is a road map, and the advice we have is that it is doable, that it is constitutional, and could be effective – it's a live option."

The Tasmanian senator has been contacting crossbench MPs over the weekend and has written to the major parties seeking their support.

He hopes to use the inquiry to pursue the grievances on behalf of disgruntled bank customers but also proposes examination of other policy issues such as the nature of the Commonwealth bank guarantee and its risk, prudential frameworks within banks, and the efficacy of current financial misconduct penalties and sentences for white-collar crime.

Senator Whish-Wilson said the Greens would not be prescriptive, emphasising that all parties would have the ability to contribute to and help design the actual terms of reference.

"They've all been out there beating the drum on this, so let's see."