Peers who backed an amendment to the Brexit bill to guarantee the rights of EU citizens have urged Conservative MPs in the House of Commons to support the change when the bill returns.

Theresa May’s government has vowed to overturn a demand by the House of Lords to guarantee the rights of EU citizens living in the UK within three months of article 50 being triggered.

However, one crossbench peer who backed the bill said she was hopeful Tory rebels would decide to defy the whip “on the basis of morality and principle” when the bill was sent back to the Commons with the amendment.

Molly Meacher said she believed “30 Tories saying they will vote to support this amendment” were considering backing the bill, though it is thought to be highly unlikely so many will ultimately do so.

Ministers were said to be disappointed by a heavy defeat in which peers voted 358 to 256 in favour of amending the Brexit bill, but made clear their position would not change on the issue.

In the Lords, seven Conservatives including former cabinet minister Douglas Hogg lined up with the Labour party, Liberal Democrats and crossbenchers to demand formal reassurances for more than 3 million EU citizens from other countries already resident in Britain.

There will now be intense pressure on Conservative backbench MPs to follow suit when the bill returns to the Commons for another vote in just under a fortnight.

“I believe it can be won in the Commons on the basis of morality and principle. Tories are principled people, generally,” Lady Meacher told BBC Radio 4’s Today programme.

Meacher said peers rejected the argument that giving EU citizens guarantees would leave UK citizens living in the EU vulnerable. “UK nationals in the EU have been getting together and putting pressure on us in the House of Lords to pass this amendment to keep this issue outside and ahead of the negotiations,” she said. “They believe and I share the belief that their only hope of getting their situation sorted out ahead of the negotiation is precisely if the British government act morally to do a deal on EU citizens.”

Campaigners will point to the fact that significant cabinet members including Boris Johnson and Andrea Leadsom have all suggested that EU citizens should have their rights protected.

But Conservative backbenchers who might be minded to rebel told the Guardian that they did not believe the amendment would remain in place.

Anna Soubry said that she was convinced by the government’s argument that this issue would be dealt with as a priority once article 50 had been triggered.

A government source told the Guardian that they took the issue of securing the rights of EU citizens very seriously, but they were determined to pass a “straightforward, simple bill”.

“The intention is to seek to overturn this in the House of Commons,” the source said.

The Lords did not go as far as calling for immediate, unilateral action but said ministers should be made to set out proposals about how they would protect citizens and their families within three months of article 50 being triggered, which is due to happen later this month.

Their decision makes the government’s Brexit bill subject to what is known as parliamentary ping pong between the Houses of Commons and Lords, delaying its passage into law by at least one week, until 14 March.

Lobbying of Conservative MPs is already under way, with cross-party talks likely as Labour and the Lib Dems urge Conservative colleagues to push for a second government defeat on the issue.

Keir Starmer, the shadow Brexit secretary, said there was a growing consensus. “The prime minister is now increasingly isolated. Labour will continue to support this simple but effective amendment when it returns to the Commons, and urge MPs on all sides of the house to do so.”

The Brexit minister Lord Bridges used the debate to tell peers that the government had been encouraged by meetings with other EU leaders who suggested that “we will indeed be able to reach a quick and timely agreement”.

But a number of peers gave short shrift to the government’s suggestion that a one-sided guarantee could be damaging for the rights of British people living in other European countries.

Labour’s Brexit spokeswoman in the Lords, Lady Hayter, opened up the debate, claiming the government had the power to act now over the issue: “In 1985, my noble friend Lord Kinnock had to say to his own party: ‘You can’t play politics with people’s jobs.’

“I now want to say to the government: you can’t do negotiations with people’s futures.”

She was backed by a number of high-profile peers including the former Lib Dem leader Lord Campbell and the former lord chief justice Lord Woolf.

The former head of the civil service Lord Kerslake said the government’s argument that an offer to EU citizens would weaken its hand in European negotiations was questionable. “However you think about that argument it is using them as bargaining chips,” he said.

Hogg, who is known as Lord Hailsham, was the most high-profile Conservative to back the amendment, laid down by the Labour frontbench but formally backed by Tories, Lib Dems and crossbenchers.

He said denying European citizens the right to remain in Britain could face legal challenge, but also said it was a matter of principle.

He described how a French waitress in parliament had asked him what would happen to her when Brexit took place. “I gave her my personal opinion, which was that there would be no problem for her, but I was not able to give her the guarantee that I think she was entitled to deserve.”

The peer reminded the House of Lords about the shock in Britain when Idi Amin expelled the Asians from Uganda.

But while there was some unexpected backing for the amendment, there was also some unlikely support for the government on the issue.

The archbishop of York, John Sentamu, said that he was one of the people who had left Uganda under Amin because of his opposition to the policy, “so I know how minorities can feel”.

But he insisted this was a simple bill only concerned with enabling May to trigger article 50, and compared it to the start of a race.

“On your marks, get set, bang,” he said. “Then they take off and it will take two years to run this race and during the running of the race we want to make sure concerns come back.”

Other supporters of the government included the former Tory leader Lord Howard, who argued that the best option to end the uncertainty was to “pass this bill as quickly as possible and to activate article 50 as quickly as possible”.

But the prime minister, who does not have a majority in the Lords, was easily beaten despite a last-minute effort by Amber Rudd to reassure peers about the government’s intentions on the issue.

She had insisted there was no question of treating European citizens with “anything other than the utmost respect”, and said their status would be top priority in EU negotiations.

The decision of peers to force a vote at committee stage was unusual, but came when it became clear the government would not make concessions on this issue.

Nicolas Hatton, the chairman of the3million campaign group which has been lobbying for the rights of EU citizens said that while he had some concerns about the amendment it was a relief that for the first time since the referendum, a majority was secured in parliament to support the rights of the 3 million EU citizens “who came in good faith to live and work the UK”.

A coalition of 13 groups representing British nationals abroad and EU citizens in the UK agreed that it was a “positive step in the right direction”.

The coalition said it was concerned that “the amendment makes no mention of UK citizens in the EEA” despite the efforts of the grassroots groups across Europe to get their message across.

The group represents more than 25,000 UK citizens in the EU including British nationals in Spain, France and Germany.

“They are also facing huge uncertainty about their futures, livelihoods and the security of their families – the same concerns facing EU and EEA citizens in the UK, whose campaign for a unilateral guarantee we fully support,” said Jeremy Morgan QC for the coalition of residents.

Monique Hawkins, a Dutch woman who highlighted the plight of EU citizens when she revealed last December she had been asked to “prepare to leave” the country after 24 years, said she was “heartened” to hear so many moving and inspiring speeches.

However, she added that she feared the successful amendment still did not cover stay-at-home parents, carers, disabled people and students whose residence status was uncertain because they decided to continue their lives in Britain but did not take out health insurance when they arrived in the country.

MPs who support Brexit will join ministers in arguing strongly that the government’s position should not cause concern among EU citizens in Britain. They point the finger instead at European countries, including Germany, which have refused to discuss any Brexit-related issues ahead of article 50 being triggered.

Steve Baker, a key figure on the Conservative backbenches who chairs the party’s European Research Group, said it was “regrettable that Germany and France are using UK citizens in their countries as bargaining chips for the Brexit negotiations”.

A spokesperson for the Department for Exiting the European Union said: “Our position on EU nationals has repeatedly been made clear. We want to guarantee the rights of EU citizens who are already living in Britain, and the rights of British nationals living in other member states, as early as we can.”