Pro-remain Liberal Democrat peers believe they could insert extra clauses into even the most tightly worded Brexit bill to force Theresa May to tell parliament more about her negotiating plans before she triggers article 50.

With the supreme court judgment on whether the government must consult parliament before invoking article 50 – the formal process for leaving the European Union - not expected until the new year, the government is thought to be quietly drafting a basic bill that its lawyers believe would be hard to amend.

But constitutional experts have told the Lib Dems there is no obstacle to adding extra clauses to such legislation, which could force the government to publish a white paper detailing how it plans to approach talks with the other EU member-states – and even offer voters a second referendum.

In a statement, four Lib Dem peers who are also QCs – including Menzies Campbell and Alex Carlile – said: “We welcome the acceptance that a parliamentary bill is likely to be needed. We shall use parliamentary procedure to ensure that the act of parliament that emerges ensures that the government has to have regard to MPs’ and peers’ reasonable expectations of the negotiation process.”

Lib Dem leader Tim Farron said: “The Liberal Democrats believe that the voters should have a say through a vote on the final deal, because departure is not the same as the destination. We will try to amend the bill and, if necessary, we will do this by proposing extra clauses to it to ensure proper debate and scrutiny of the process and the issues.”

Labour has said it will not join any collective effort to delay or block an article 50 bill, and shadow chancellor John McDonnell has described Brexit as an “opportunity”.

But Labour sources have suggested that this would not rule out the party’s peers backing clauses that would oblige May to report back to parliament regularly on her progress, for example – something that need not cause a delay.

The government is appealing against the high court judgment in the case brought by Gina Miller over whether the government could invoke article 50 using its prerogative powers, without winning parliament’s backing.

May has set herself a deadline of the end of March for triggering article 50, which would leave the government a tight timetable for getting legislation through both houses of parliament if it loses the supreme court case.

In the House of Commons, few MPs have said they would vote against a brief bill triggering article 50 — but even some Conservatives privately suggest they might withhold their support unless the government is clearer about its negotiating stance.

The supreme court case will be heard by all 11 justices because of the seriousness of the issue. One of them, Brenda Hale, caused controversy on Tuesday by discussing the case in public at a lecture in Kuala Lumpur.

Critics including former work and pensions secretary Iain Duncan Smith condemned her decision to speak about the appeal, and warned of a “constitutional crisis” if the supreme court upheld the high court’s verdict.

But in an interview with Solicitors Journal on Wednesday, Lady Hale defended herself by insisting she had simply offered a neutral explanation of the issues at stake. “I have exhibited no bias and those that suggested that I have are simply mistaken,” she said.

Hale also lamented the negative press coverage of the high court judgment, which saw the judges who ruled on the case referred to as “enemies of the people”.

“It is unfortunate that it isn’t made clear to the British public, because it is very important they understand what the role of the judiciary is, which is to hear cases in a fair, neutral, and impartial way,” she said. “You have to be independent and true to your judicial oath and cannot allow yourself to be swayed by extraneous considerations that have nothing to do with the law.”