Campaigners for the rights of Britons in the EU have described Theresa May’s failure to mention them in her statement on the Brexit negotiations as “disgraceful” and called on the UK and the EU to both guarantee their entitlements after Britain leaves.

Speaking on Friday, the prime minister told EU citizens living in the UK that “even in the event of no deal, your rights will be protected”. Downing Street later confirmed “further details will follow” regarding this guarantee.

But in a letter to the prime minister, Jane Golding, the chairwoman of British in Europe, said: “Over the past 18 months the UK has negotiated away our rights, you and your secretaries of state have refused to meet us and now you completely ignore us at a critical time in the negotiations.

“We are and we remain British citizens. You have obligations towards us and we expect you and your government to respect and honour those obligations.”

Referring to May’s demand that the EU treat the UK with respect, Golding said the prime minister needed to show this to British people living in other EU countries.

They called on her and the EU’s chief Brexit negotiator, Michel Barnier, to “ringfence” the deal on citizens and remove it from the talks, a course of action supported by the3million, a lobby group that campaigns for EU citizens in the UK.

It was among the organisations that gave a cautious welcome to the prime minister’s promise to unilaterally guarantee their rights to live and work in the UK in the event of no deal.

“If that is what she is going to do, then we will be very happy,” said Nicolas Hatton, the founder of the3million.

May’s move puts pressure on EU leaders to reciprocate by offering to guarantee the entitlements of the estimated 1 million Britons living in the EU.

But Hatton warned an EU-wide deal or a series of bilateral agreements would be required in order to retain the full range of social and employment rights, including pension payments and recognition of professional qualifications.

“If she is saying ‘let’s take EU citizens off the table’, then she is going in the right direction and we welcome that,” he said.

The campaigner added that it would have to “involve a deal for British in Europe as well, which she didn’t mention in her speech”.

Stijn Smismans, professor of European law at Cardiff University, said that if May was to swiftly deliver on her promise and guarantee all rights, she would need to propose a deal with EU leaders under the article 50 procedure. “This could then be adopted by a qualified majority in the European council and ratified by parliament and that way the rights are guaranteed in a treaty,” he said. This would also seal the rights of Britons living in the EU.

The prime minister’s pledge on EU citizens came after the former president of the Confederation of British Industry said May and EU leaders should be “ashamed” that citizens’ rights were still part of the negotiations.

Roger Casale, the founder of New Europeans, a campaign group, said May’s statement “will be a huge relief to the millions whose life plans had been thrown into jeopardy by the Brexit vote”.