Critics of the Brexit bill are increasingly confident that they will be able to win a vital parliamentary battle in the House of Lords, a senior opposition peer said on Tuesday.

Dick Newby, the leader of the Lib Dems in the Lords, said he was confident that enough peers would back amendments on issues such as the rights of EU citizens and parliamentary votes on the final Brexit deal to defeat the government and force a rethink.

He spoke on the same day that Brexit secretary David Davis admitted that he expected the bill to “ping pong” back to the House of Commons with amendments over the next fortnight.

The Brexit bill was passed by MPs last week without amendment despite the efforts of Labour, the Lib Dems and a handful of rebel Conservatives.

Newby said he expected around 230 Labour and Lib Dem peers to back an amendment on EU citizens, as well as most of the crossbenchers and at least two Tory peers. With a number of Tory peers also expected to abstain, he said those numbers should easily defeat the government.

“There are a lot of members of the group for whom Europe is the big thing that has motivated them in politics,” he told the Guardian. “We were complacent, truth be told. But things have turned and people on our side feel very strongly about it.”

Newby said all peers had been told to cancel leave or prior engagements. “There are very, very few votes where we say to people, ‘I don’t care that you’ve got a lecture tour of the States’ because, normally, if people have longstanding commitments you let them off,” he said. “But I don’t think [Lords chief whip] Ben Stoneham is going to be very accommodating to anyone.”

Labour has promised no “extended ping pong” as it does not want to frustrate the timetable for triggering article 50, but it has laid eight amendments on issues from EU nationals to quarterly reporting to parliament about the Brexit process.

However, Newby said he believed Labour peers were more independently minded and many could even be persuaded to back a Lib Dem amendment on a second referendum, given the timing of the Lords vote after the crucial Stoke and Copeland byelections.

“We’ve got three weeks to persuade them,” he said. “What have they got to lose? There are very many strong Europeans in the Labour party. They all know Corbyn is taking the Labour party down a destructive path, they are all beside themselves.”

Newby said peers may be prepared to be more openly pro-European than Labour MPs because they did not have to answer to constituencies. “What’s the point? If you’re 65 and a Labour peer and been pro-European all your life, why just sit on your hands? A lot of them are taking it into their own hands, because I talk to a lot of them.”

Labour peer Peter Hain, a former cabinet minister, has tabled several amendments, including one on the Northern Irish border, which Newby said was gaining traction.

Ann Linde, Sweden’s minister for EU affairs and trade, with David Davis at a joint press conference in Stockholm. Photograph: Maja Suslin/EPA

Labour amendments include one backed by crossbench peer Lord Pannick, the QC who opposed the government at the supreme court over the need for parliamentary approval of the triggering of article 50. Pannick’s amendment would require a parliamentary vote on the final Brexit deal, specifying that it should take place before any deal is approved by the European commission or parliament.

Threats that the government would reform the Lords if it did not pass the bill quickly were empty, Newby said. “There is zero capacity in Whitehall to worry about House of Lords reform, it’s ludicrous to even contemplate it,” he said.

Speaking in Stockholm about the bill’s progress through the Lords at a joint press conference with Swedish minister for EU affairs and trade Ann Linde, Davis said he still expected Theresa May to be able to trigger article 50 notifying the EU of the UK’s intention to leave by the end of March.

However, Davis said he was also expecting that the upper house “will do its job of scrutiny, we’ll have some passing backwards and forwards, we call it ping pong, you can imagine why, backwards and forwards of the bill, but I expect that to be resolved in good time before the end of March”.

Davis said he was confident article 50 would be triggered on the government’s timetable, but that did not mean the formal notification would be given at the scheduled summit of EU leaders on 9 March.

Newby said he believed that it would be near to impossible to trigger article 50 on 9 March, but it would be possible by the following week. “My guess is that it could be in the Commons on the 13th and back here on the 14th,” he said. “There will not be a stomach to keep sending it back on most things. You can often get an agreement that meets in the middle, but with EU citizens that is more difficult because either you guarantee them the rights or you don’t.”

Speaking alongside Linde, Davis said he wanted to reassure EU citizens living in the UK that the government wanted discussion of their rights, and those of Britons on the continent, to be the first item on the negotiating table, including issues such as their social support and healthcare. “I don’t see any reason for anybody else to hold this up, once the negotiation starts properly,” he said.

However, the UK government has refused all calls to unilaterally guarantee the rights of EU citizens in the UK without similar assurances for British citizens in the rest of the EU. On Monday the Guardian reported that a leaked EU document had warned that British citizens on the continent could face a backlash as a result of the UK’s treatment of European nationals since the referendum.

Linde raised concerns at the press conference about the rights of EU nationals in the UK, pointing out that about 100,000 Swedes live in the UK and 30,000 Britons reside in Sweden, saying they “must not become a bargaining chip” in the Brexit negotiations.

On Tuesday the finance ministers of Scotland, Wales and Northern Ireland branded quadrilateral Brexit talks with the chief secretary to the Treasury, David Gauke, as disappointing, accusing him of failing to provide enough information on how exiting the EU would affect their nations. During the talks, held in Edinburgh, the ministers urged the UK government to keep the needs of their regions at the heart of any Brexit negotiations.

Scotland’s finance secretary, Derek Mackay, said that keeping Scotland in the European single market was “absolutely essential for Scottish jobs, investment and long-term economic wellbeing”. Welsh finance secretary Mark Drakeford similarly called for “unfettered access to the single market” for Wales.

Stormont finance minister Máirtín Ó Muilleoir said that nothing he had heard during the meeting had changed his view that the UK government had failed to understand “the calamitous effects” that Brexit would have on Northern Ireland’s economy. “There has been no appreciation of the need for a special status for the North within the EU,” he said.