EU citizens in the UK have protested that Theresa May’s “generous” offer will leave them with fewer rights after Brexit than “British jam”.

The Prime Minister’s proposals also ran into trouble from other EU leaders who warned of “open questions” and a “long, long way to go” before agreement.

The obstacles emerged after Ms May told a Brussels summit that she was willing to give the 3m EU citizens in Britain a new “settled status”, allowing them to stay if they have lived here for five years.

People gaining it would secure rights on healthcare, education and benefits broadly similar to those enjoyed by EU citizens in the UK currently.

But Ms May refused to reveal the cut-off date after which new arrivals will no longer be guaranteed the status, leaving many people uncertain of their UK residency.

And, crucially, she has vowed to fight the EU’s demand that future rights must be guaranteed by the European Court of Justice (ECJ) – a certain flashpoint over the months to come.

The 3million group, which represents EU citizens in the UK, described the offer as “neither fair or really serious”.

“We really fear the loss of access to the ECJ,” said Anne-Laure Donskoy, a founding member.

“Under any kind of trade deal, there has to be a supranational court to give the people trading protection, so we do not have unilateral future changes.

“British jam and the French wine trade will be regulated under this kind of jurisdiction, whereas we will lose this. Why should jam have more rights than a Spanish nurse, or a Polish plumber?”

Ms Donskoy also criticised the refusal of the British Government to talk with the group, although it will, finally, meet with Brexit Secretary David Davis next week.

“The EU has been much more forthcoming in inviting us to have a conversation with them,” she said – including with Michel Barnier, the EU’s chief Brexit negotiator.

At the summit, Austria's Chancellor, Christian Kern, warned: “There are so many details left open.

“A lot of citizens of Europe are concerned and are not covered with the proposals of Ms May, so there is a long, long way to go for the negotiations.”

Arriving for the second day of the summit, on the anniversary of last year’s Brexit referendum, Mrs May acknowledged that elements of her plans had put her on a collision course with the EU.

“Of course, there will be details of this arrangement which will be part of the negotiation process,” she said.

But, she insisted: “I want to reassure all those EU citizens who are in the UK, who have made their lives and homes in the UK, that no-one will have to leave, we won't be seeing families split apart.

“This is a fair and serious offer. I want to give those EU citizens in the UK certainty about the future of their lives, but I also want to see that certainty given to U citizens who are living in the EU.”