Labour’s leader in the House of Lords, Angela Smith, has said the government is “clinging to office by its fingertips” after the DUP withheld its support in a series of key votes.

“They’re not in charge,” said Lady Smith. “The government is hanging on.”

Downing Street has said the confidence-and-supply arrangement that underpins Theresa May’s working majority in the House of Commons remains in place, despite the DUP having abstained or even backed Labour in several votes on the finance bill.

However, senior Conservatives say Andrea Leadsom, the leader of the Commons, is “very concerned” about the deteriorating relationship between the Tories and the DUP and is pressing for the matter to be resolved urgently.

Meanwhile, Whitehall departments piloting legislation through parliament risk being forced to negotiate with the chief whip, Julian Smith, about what concessions they will have to accept to prevent the government facing a string of defeats.

Labour points to mounting evidence that the government is taking action to avoid a repeat of the close shave on Monday night when its majority was cut to just five on one Labour amendment to the finance bill.

On Wednesday the government made a concession in the mental capacity bill passing through the Lords, dropping proposals that would have given care home managers new responsibilities for their residents’ care.

Until Wednesday the government had staunchly defended its plans, but Smith suggested it was keen to avoid a potential defeat when the bill returns to the Commons.

Discussions are also under way on a potential climbdown over the counter-terrorism and border security bill. “What we’re finding is it’s easier for us to press for amendments,” Smith said.

Separately on Wednesday, the junior sports minister Mims Davies and her civil servants were forced back to the drawing board on an overhaul of betting on horse racing after a joint committee of the Lords and Commons rejected the government’s attempt to pass sweeping changes without primary legislation.

Two key pieces of Brexit legislation – the customs and trade bills – have been awaiting scrutiny by peers since before the summer recess, but the government has not yet allocated any time for them to do so.

And in the coming weeks MPs need to vote on the managed migration of universal credit, which will allow existing claimants of other benefits to be moved on to the new system. Regulations to implement the change have been put before parliament but no date has been set for them to be voted on.

Westminster insiders believe the new work and pensions secretary Amber Rudd’s emollient tone on universal credit, including suggesting the controversial five-week waiting time for payments could be reviewed, is aimed at winning support in the vote.

The DUP threw May a lifeline in 2017 after the general election wiped out her majority, by offering to support the Conservatives on key issues including Brexit and budget votes.

But by abstaining from a series of key votes on the finance bill on Monday and Tuesday in protest over the Brexit deal, they breached the terms of the agreement and raised questions about May’s ability to govern.

However, Labour is not planning to table a vote of no confidence in the government before May brings her Brexit bill back to the Commons for the meaningful vote, fearing that it would risk uniting the Conservatives behind the prime minister.

The shadow chancellor, John McDonnell, said on Wednesday that if the government’s deal was rejected in a meaningful vote next month, May would return to Brussels to seek concessions. If it fell again then Labour should be given the chance to form an administration, he said.

“At that stage we will be saying: give us the opportunity. You’re a minority party, give us the opportunity to take over and see if we can form a government – a minority but with a majority position in parliament,” McDonnell said.

“If that’s denied us then we will be pressing for a general election, but as you know you need that two-thirds majority. It’s very difficult to get. Anything could happen at that stage.” ﻿