If the government survives a vote of no confidence, Labour could begin campaigning for a second referendum on remaining in the European Union, the shadow Brexit secretary Keir Starmer said Sunday.

"It seems to me that if the Prime Minister has lost a vote of that sort of significance, then there has to be a question of confidence in her government," Starmer told Sky News , referring to the December 11 vote scheduled in the House of Commons for May's Brexit bill.

Now back from G20 talks, May has just one week to convince dissenting members of Parliament to pass the bill, a feat the country's pro-Brexit Environment Secretary Michael Gove concedes will be "challenging."

Gove told the BBC Sunday that if ministers don't pass the bill "the alternatives are no deal or no Brexit."

The likelihood of rejection could increase Monday if Labour is successful in forcing May to reveal the full legal advice she sought before agreeing the deal with European leaders last month

The UK's attorney general, Geoffrey Cox, is due to brief lawmakers on the matter Monday, but Downing Street is seeking to avoid publishing the full advice, in defiance of a Commons vote last month obliging it to do so. The government argues Cox's briefing will be sufficient, but Starmer said "if they don't produce it tomorrow then we will start contempt proceedings, and this will be a collision course between the government and Parliament."

"I accept that it's exceptional to have that disclosed. It has happened in the past, but it is exceptional," he added. "That's why we had a debate in parliament, to say: is this the sort of case where it's so exceptional that it should be disclosed?"

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This will put May in a difficult position as she attempts to lobby Conservative Party votes for her bill, while potentially having to reveal compromises over the so-called Northern Ireland "backstop" position which could doom it in the eyes of pro-Brexit MPs.

The backstop is designed to prevent a hard border between EU member the Republic of Ireland, and Brexiting Northern Ireland -- which many fear could lead to a return to violence in the region. Under the agreement reached with Brussels , failure to reach an alternate deal defaults to a backstop in the form of a "single customs territory between the (European) Union and the United Kingdom."

Such a situation would essentially leave the UK both in and out of the EU, in line with all EU regulations and rules but unable to influence them. It would also block the most ambitious post-Brexit policies of hardliners in May's Party, many of whom see such a deal as anathema to the 2016 vote on leaving the EU.

As if the Northern Ireland issue wasn't bad enough for May's chances, the government was also forced to admit last week that the deal will be bad for the UK's economy . According to assessments by Downing Street and the Bank of England, under any scenario, leaving the European Union will make Britain poorer than staying in.

In the increasingly likely event therefore that May loses next week's vote, Labour will almost certainly seize on it as an opportunity to bring down her government -- which is currently propped up by an unsteady alliance with the right-wing Northern Irish Democratic Unionist Party (DUP), that is itself expected to vote against the deal.

"Obviously, it'll depend on what actually happens in nine days. It depends on what the response is. But if she's lost a vote of this significance after two years of negotiation, then it is right that there should be a general election because, but for the Fixed-term Parliaments Act, the convention was always, if a government loses what's called a confidence vote -- something of such significance -- then that government has to go," Starmer said.

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Under the Fixed-term Parliaments Act 2011, the government in theory has a five-year term, but a vote of no confidence or a vote by two thirds of the Commons can still trigger a general election at any time, making it exceedingly difficult for the government of the day to stave off an election should lawmakers wish to go to the voters.

"Obviously, if that doesn't happen, we need to press on to other options such as a public vote because, having gone through the first two options, we would need to look at what happens then," Starmer said.

Such a situation, while it would ramp up pressure on May's government, would likely be preferable to the Prime Minister, who has previously attempted to paint Labour as untrustworthy on Brexit and allow her to shore up support among Euroskeptic voters across the political spectrum.