Theresa May is facing a fresh Brexit showdown after Jeremy Corbyn said Labour would support an amendment on EU citizens’ rights that already has the backing of 130 MPs including 60 Conservative backbenchers, some of whom are Eurosceptics.

If selected by the Commons Speaker for a vote on Wednesday, there would be a “comfortable victory” on a “very uncontroversial issue”, said the Conservative MP Alberto Costa, who tabled the amendment.

It seeks to ringfence the rights of all British nationals settled in the EU and those of EU citizens in the UK, regardless of the outcome of the Brexit negotiations.

“This is not about the single market or the customs union, this is about the rights of innocent people, most of whom did not have a say in the referendum, including British nationals in the EU,” said Costa.

It has been backed by the Eurosceptics Jacob Rees-Mogg, Sir Edward Leigh, Steve Baker and Sir Graham Brady, but also by staunch pro-EU backbenchers including Sir Oliver Letwin and Dominic Grieve.

Corbyn confirmed he would be backing the amendment minutes after May moved to head off the rebellion in a statement to the Commons committing to votes on a no-deal Brexit or a delay.

May urged the remaining 27 EU member states to match the “guarantee” the UK had made to EU citizens. “The EU does not have the legal authority to do a separate deal on the EU citizens’ rights without a mandate … If it’s not within that withdrawal agreement then it is a matter for individual states, and we have already taken that up with individual states,” she said.

Costa said May was hiding behind process, adding: “If she says the [European] commission can’t do it, what she needs to do is go to all the EU leaders and get them to tell the commission to take it off the table.

“She promised to protect citizens’ rights more than two years ago and has failed to do so. The EU have asked us what we want and we will show them this is what we want.”

Others supporting the amendment include Iain Duncan Smith, Dominic Raab, Nigel Evans, Zac Goldsmith, Craig Mackinlay, Anna Soubry and Justine Greening.

It calls on May to seek at “the earliest opportunity a joint UK-EU commitment to adopt part two of the withdrawal agreement on citizens’ rights and ensure its implementation prior to the UK’s exiting the European Union, whatever the outcome of negotiations on other aspects of the withdrawal agreement”.