By Marine Strauss

STRASBOURG (Reuters) - European Union chief negotiator Michel Barnier warned Britain on Tuesday not to discriminate against EU citizens seeking permanent residency after Brexit, urging London to set up an independent monitoring authority.

He was speaking after members of the European Parliament voiced concern that Britain's imminent exit from the European Union could endanger the rights and protection of many of the 3.5 million EU citizens living there.

"I will continue to insist on the particular importance of the UK putting in place a strong, independent monitoring authority...that must be able to act rapidly and fairly when faced with complaints from EU citizens and their families," Barnier told European lawmakers in Strasbourg.

With Brexit, due to take effect on Jan. 31, the British government is introducing the biggest shake-up of its border controls for decades, ending the priority given to EU migrants over those from other countries.

Under the divorce agreement reached between Britain and the EU's other 27 member states last year, EU nationals living in the UK have until June 2021 to apply for permanent residence.

"We must now work toward proper implementation of these rights and we won't be accepting any half measures or any form of disguised or veiled discrimination," Barnier said.

Britain's Home Office, the ministry responsible for immigration, did not have any immediate comment.

Reuters reported in November that Britain was threatening to deport EU citizens if they failed to apply on time and would grant leniency only in exceptional circumstances.

In a letter to Brexit Secretary Steven Barclay, which was first reported by the Telegraph last week, Barnier said he was concerned about "conflicting signals" on what would happen to those who fail to register for settled status by June 2021.

He called for a "generous interpretation" of such cases to avoid criminalization and deportations, the Telegraph said.

European Parliament members expressed worries during a debate on Tuesday that Britain would not honor commitments of the agreement, and European Commission President Ursula von der Leyen told them it was "a legal issue with a moral imperative".

Barnier said the European Commission expected Conservative Prime Minister Boris Johnson's government to help EU citizens meet administrative requirements and accept requests that fail to meet the deadline for good reasons.

Von der Leyen said that about 2.5 million EU citizens living in Britain had applied for residence status and most of them have been granted the right to remain.

But she said there are many cases - even people who have lived there for 40 years or more - of applications being held up by requests for further information.

(Additional reporting and writing by John Chalmers in Brussels; Editing by Mark Heinrich)