The EU on Monday said it was taking Britain to the European Court of Justice for infringing rules on the free movement of the bloc's citizens and their family members after Brexit.

The European Commission said it believed that "there were several shortcomings" in Britain's implementation of treaties at the end of 2020.

"The European Commission decided to refer the United Kingdom to the Court of Justice of the European Union... for failure to comply with EU law on free movement of EU citizens and their family members at the end of 2020," the commission said in a statement.

The legal action comes as the Labour government elected this year has sought to "reset" relations with Brussels after years of post-Brexit rancour under previous Conservative administrations.

British Prime Minister Keir Starmer held talks with commission chief Ursula von der Leyen in Brussels in October, and this month Finance Minister Rachel Reeves became the first British chancellor since Brexit to attend a meeting of eurozone counterparts.

The case was initiated in May 2020, when the EU sent a letter of formal notice to Britain complaining that national legislation limited the scope of beneficiaries of EU free movement law.

Despite exchanges with London, the commission said that "several elements of the grievances remain unaddressed including on the rights of workers and the rights of extended family members" - warranting legal action.

Britain formally left the EU on January 31, 2020. 

But under the "Withdrawal Agreement", EU citizens and their family members who moved to Britain before the end of 2020 were granted broadly the same rights they had before Brexit.