Politicians on both sides of the English Channel are eager to resolve the plight of millions of people living in a state of limbo thrown up by Britain's decision to leave the European Union(EU), British Prime Minister Theresa May made clear Monday.

May told Members of Parliament (MPs) in the House of Commons that her counterparts in EU countries had not resolved their status ahead of formal talks.

As a curtain raiser to a round of discussions in the House of Commons this week over the triggering of Britain's exit from Brussels, May spoke of the millions of British people living in EU countries and the millions of Europeans living in Britain.

It was an issue discussed by May last week when she met leaders of the other 27 EU member states in Malta.

Labour leader Jeremy Corbyn told the House of Commons Monday, "There is no need to wait for negotiations to begin, the government could do it now. This is not a question about Brexit, it is a question about human rights, democracy, and decency towards people who have lived and worked in this country."

Corbyn added: "Many families have had children born here, and I think we must guarantee their rights. Many of those people have been left in limbo, and are very deeply concerned and stressed."

On the millions living on the European side of the English Channel, May said: "I think it is right that we ensure that the rights of UK citizens living in other European states are maintained. It is clear from the conversations that I have had with a number of European leaders that they think that it should be dealt with in the round as a matter of reciprocity."

She referred to discussions she had had with Spanish Prime Minister Mariano Rajoy, saying it was very clear that "we want to give reassurance to people as early as possible in the negotiations."

Conservative MP John Redwood asked May if she was shocked that the EU was unable to offer a simple reassurance to all British citizens living in EU countries that they would not face eviction.

May said she had every confidence the issue would be addressed early on in the negotiations.

"I would have liked to be able to address it outside the negotiations but, sadly, some member states did not wish to do that. However, I think that the goodwill is there to give that reassurance to EU citizens here and to UK citizens in Europe."

MPs are this week discussing details of the Article 50 Brexit bill -- the formal process by which Britain will leave the bloc -- before it goes to the House of Lords.

Although amendments are likely to be made and changes recommended to the legislation, May's government is confident it will win enough support to gain the consent of Queen Elizabeth II to trigger the exit process next month.