Manchester United striker Mason Greenwood has admitted he made "a huge mistake" after he was axed from the England squad for breaching COVID-19 protocols to meet two women while on international duty in Iceland.

Greenwood, 18, and teammate Phil Foden, 20, have been sent home by manager Gareth Southgate after it was revealed the pair left the team's secure bubble to meet two women in the public area of the England hotel on Saturday night -- just hours after making their international debuts in the UEFA Nations League victory over Iceland.

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Greenwood, who will be the subject of investigations by the Football Association and United, has apologised for "the embarrassment" surrounding the incident in a statement released on the club's website on Tuesday.

"Having now had the chance to reflect on what's happened, I can only apologise to everyone for the embarrassment I have caused," Greenwood said.

"It was irresponsible of me to break the COVID-19 protocols which are in place to protect players, staff and the public.

"In particular, I want to apologise to Gareth Southgate, for letting him down, when he had shown great trust in me.

"Playing for England was one of the proudest moments in my life and I only have myself to blame for this huge mistake.

"I promise my family, the fans, Manchester United and England that this is a lesson I will learn from."

Greenwood and Foden will play no part in England's game against Denmark in Copenhagen on Tuesday night.

Both players have returned to their clubs, and while neither are expected to have to quarantine because of UK government rules for travellers from Iceland, they could yet face disciplinary measures before being allowed to return to training.

"On this occasion I made a poor decision and my behaviour didn't meet the standards expected of me," Foden said in a statement on Monday.

"I breached COVID-19 protocols put in place to protect myself and my England colleagues. As a consequence I will now miss the opportunity to travel to Denmark with the squad, and that hurts.

"I will learn a valuable lesson from this error in judgment and I wish Gareth and the team good luck this week."