Two independent MPs have heaped more pressure on the Turnbull government to take tough action against banks.

Crossbenchers Bob Katter and Andrew Wilkie on Monday introduced to parliament separate private bills calling for greater scrutiny of the sector.

Mr Wilkie is concerned there’s no complaints mechanism for customers that isn’t run by the industry, and that legal action is the only – and often unviable – option.

His proposal would make an existing voluntary code of practice mandatory and give the banking regulator more power to issue penalties for breaches.

“It would give banking customers some rights when dealing with their financial institutions,” he told MPs.

It’s the second time Mr Wilkie has tried to put forward such laws, having made an attempt in 2012 under Labor.

Mr Katter’s bill would establish a commission of inquiry into the banking and financial services sector, specifically looking at unethical, unlawful and improper conduct.

It would have the same powers as a royal commission, as well as additional powers relating to the protection of whistleblowers.

Mr Katter slammed the cowardice of politicians who have run away from the issue but praised the “courage and intellectual integrity” of Nationals MP George Christensen, who sat with the crossbencher on Monday in support of the bill.

“Everyone agrees to this except the Liberal Party … and their isolation is standing out now like a neon light,” Mr Katter told the lower house.

Last week, the Greens introduced a bill in the Senate to establish a similar commission of inquiry.

The proposal has the support of Labor and most of the crossbench, as well as Nationals senator John Williams who vowed to cross the floor.