The Opposition Leader has personally written to each of the 16 Senate and lower house crossbenchers asking for a one-on-one meeting, telling them that after last week's parliamentary testimony by the big four bank chiefs Labor is "more determined than ever" to get a royal commission over the line.

"A once-a-year, three-hour meeting of a Liberal-dominated committee does not do the job," Mr Shorten tells them.

"Instead of answers, we got self-serving lectures, excuses and obfuscation.

"I would like to meet with you to discuss how we can work together to deliver justice for the tens of thousands of Australians who are victims fo banking and financial services misconduct – and to ensure such illegal and unethical behaviour cannot occur again."

The letters are a sign Labor has no intention of ditching the issue and will seek to keep the pressure on the Prime Minister when Parliament resumes on Monday.

Same-sex marriage will also be high on the agenda, with Labor expected to confirm it will oppose Mr Turnbull's public plebiscite plan, with a final decision to be made at shadow cabinet meeting on Monday and signed off by the party room on Tuesday.

The government will seek to shift the focus to unions and the building industry with its double dissolution legislation.

Mr Turnbull confirmed last week he plans to establish a new low-cost tribunal for banking victims in what is being seen as his latest attempt to stave off a Labor's popular push for a powerful – and potentially damaging – royal commission.

The Greens, Nick Xenophon, Jacqui Lambie and One Nation already support the idea of a royal commission – and indeed helped Labor embarrass the government last month by teaming up to pass an upper house motion in favour of it.

The same motion almost made it through the lower house when Labor ambushed the government after several Coalition MPs left work early. That has led to stringent new rules about when Coalition MPs can leave Parliament House.