The European Union's lead Brexit negotiator has given a cool response to Britain's offer on European Union citizens’ rights in Britain after it leaves the union, saying the EU wanted to get the same level of rights as under EU law.

"EU goal on citizens’ rights: same level of protection as in EU law. More ambition, clarity and guarantees needed than in today's UK position," Michel Barnier said in a tweet.

British Prime Minister Theresa May unveiled details of her plan to protect the rights of EU citizens living in Britain, saying the government would work to offer them the same health, medical and educational benefits as British citizens.

An agreement on the post-Brexit rights of EU nationals is one of the easier issues for the two sides to agree on, with both Britain and the rest of the bloc wanting to provide assurances to millions of their citizens living abroad.

But the British proposal says that once Britain leaves the EU, the EU's top court, the Court of Justice of the European Union, would no longer have jurisdiction in the United Kingdom in cases involving EU citizens.

This is problematic for the EU, because EU citizens in Britain, who now can appeal decisions of British courts to the European Court of Justice, would lose that right with Brexit, meaning they would be worse off than now.

Some EU officials welcomed some elements of the proposal.

"At first glance, there is at least one element which makes a difference - namely the commitment to simplify the existing administrative procedures," the European Parliament's chief Brexit negotiator, Guy Verhofstadt, said.

"However, a number of limitations remain worrisome and will have to be carefully assessed," he said in a statement.

"The European Parliament will act to protect the rights of EU citizens in the UK and defend the integrity of European Union law, including the Charter of Fundamental Rights and its enforcement framework," he added.