The Conservative backbencher who stunned his own colleagues with a cross-party victory for a no-deal Brexit amendment on EU citizens’ rights is seeking an urgent meeting with Donald Tusk.

He is writing to the president of the European council over a new instruction to Michel Barnier’s team in Brussels to start working on ringfencing the rights of EU citizens in the UK and British nationals in the rest of the EU in the event of no deal.

Alberto Costa, who was forced to resign even though his 11th-hour parliamentary amendment was accepted by the government, said: “Last night was an amazing moment. I’m totally proud that a little lowly backbench MP like me has been able to unite the House of Commons on this contentious Brexit issue over one of the least contentious subjects and bring the government to the dispatch box and vote in favour.”

He added: “I’ll be writing to Donald Tusk seeking a meeting with a cross-party delegation from parliament to ask him to engage in a positive manner with the European council and ask him to give serious consideration to a unanimous mandate for the European commission to carve out part two of the withdrawal agreement on citizens’ rights and have it as a special treaty in international law.”

Conservative MP Alberto Costa with members of the3million group after his amendment on EU citizens rights was taken up by the government. Photograph: the3million

Campaign groups British in Europe and the3million in the UK who had met Costa just a few weeks ago to press their case said they were delighted with the amendment.

British in Europe (@BritishInEurope) Tonight we did it. Through the solidarity of BritishinEurope and @the3million working together, we persuaded the UK Parliament to make the UK govt push for our rights to be ring fenced whatever the outcome of Brexit pic.twitter.com/cfzKpXIDmk

In an extraordinary development on Wednesday Costa was forced to quit his job for speaking out but hours later won cross-party support for the amendment.

Many now believe he should be reinstated as parliamentary private secretary to the Scottish secretary, David Mundell, but Costa says he doesn’t “give a stuff about being a junior aide” and if he had to resign over the rights of 5 million people “so be it”.

UK House of Commons (@HouseofCommons) Commons approves @AlbertoCostaMP's Amendment (b) to the #BrexitNextSteps motion without a division

This requires the PM to seek a joint UK-EU commitment to adopt part 2 of the Withdrawal Agreement on citizens' rights whatever the outcome of negotiations on other parts of the deal pic.twitter.com/PzRd7yhHfS

Costa’s move seemed to hit quicksand after he tabled the amendment, with Theresa May indicating government disapproval. She told the house the EU had said ringfencing rights across the bloc was unworkable as they did not have “legal authority” to do so.

After consulting Prof Stijn Smismans, professor of EU law at Cardiff University, Costa confirmed that the commission did not have the authority but that was to miss the point.

Smismans, pointed out that the European council “can revise that mandate at any time. There is no legal hurdle at all”.

As part of the plan Costa also wants the no-deal citizens’ treaty to have a transition period, as originally envisaged up to the end of 2021 at least.

This would enable the resumption of negotiation on citizens’ rights that were omitted from the withdrawal agreement because they were due to be part of the second phase of Brexit negotiations on freedom of movement issues and the future relationship between the EU and the UK.

This would be a boon for the estimated 1 million British nationals in Europe who, as it currently stands, will not be allow to work or offer a service in a second member state. It prevents, for example, British nationals who live in Germany or Belgium, entering Luxembourg to work, and prevents British nationals in Spain or Italy offering services ranging from accountancy to law to translation to do so from their home state.