Tammy Abraham, Ben Chilwell and Jadon Sancho could miss England’s game with Wales on Thursday after being told to stay away from St George’s Park.
They could now miss the game at Wembley because of Uefa’s testing protocols.
To have any chance of playing they need to complete a coronavirus test 48 hours before Thursday’s 20:00 BST kick-off.
However, having already been told by the Football Association (FA) to delay their arrival at England’s training camp, completing a test in time appears unlikely.
The FA says the delay is a precaution while it assesses if there is any risk to the wider group.
Police will not be taking any action against the trio.
“As a matter of course we are not investigating Covid-related issues retrospectively,” said a Metropolitan Police spokesperson.
Chelsea forward Abraham, Chelsea left-back Chilwell, 23, and Borussia Dortmund winger Sancho, 20, have all apologised for the breach.
Abraham said he was unaware the party was planned but “deeply regrets” it and has apologised for “the naivety shown”.
In a post on Instagram, Sancho wrote: “I would like to apologise for breaking the government guidelines and although I was unaware upon arriving of the numbers attending, I take full responsibility for my actions.
“I will make sure moving forward that I learn from this.”
The party, which was first reported by the Sun, happened hours after Abraham played in Chelsea’s 4-0 win over Crystal Palace on Saturday.
Police have the power to break up groups larger than six and those who ignore officers could be fined £100 – doubling with each offence to a maximum of £3,200.
It is understood those at the party were close friends and family who had their temperatures checked on arrival.
“On Saturday evening I arrived home to find a small surprise gathering had been organised for me with family and close friends to celebrate my birthday,” Abraham said.
“Although I was totally unaware this was planned, I would like to wholeheartedly apologise for the naivety shown by all for the organisation and attending of this gathering.
“I recognise that I have a responsibility both in my professional and personal life to honour and respect the guidelines and deeply regret that this took place.
“All I can do now is learn from it, apologise to everyone and ensure it never happens again.”
On Monday, Chilwell also posted on social media, saying: “I would like to apologise for my lack of judgement over the weekend.
“I have a responsibility to respect the guidelines. I will ensure I learn from this and will not put myself in this position in future.”
The rest of England manager Gareth Southgate’s squad have arrived at St George’s Park to prepare for three games in a week at Wembley.
After the friendly against Wales, England host Nations League fixtures against Belgium and Denmark on 11 and 14 October respectively.
Last month, Manchester City midfielder Phil Foden and Manchester United forward Mason Greenwood were dropped from an England squad after an “unacceptable” breach of Covid-19 quarantine guidelines in Iceland.
Southgate was already planning to talk to his squad this week about “what it means to wear the shirt”, following the incident involving Foden and Greenwood.
Southgate plans to give his players “some reminders on how we work”.
“That’s not a case of reading the riot act,” he said last week. “That’s a case of asking the players what sort of team they want to be involved in and be a part of.”
Manchester City forward Raheem Sterling has been ruled out because of injury, with Chelsea full-back Reece James promoted to the senior squad from England Under-21s.
Wales will be without Juventus midfielder Aaron Ramsey because the Serie A side have put their squad into a bubble after two non-playing staff members tested positive for Covid-19.
Full England squad
Goalkeepers: Jordan Pickford (Everton), Nick Pope (Burnley), Dean Henderson (Manchester United)
Defenders: Trent Alexander-Arnold (Liverpool), *Ben Chilwell (Chelsea), Conor Coady (Wolves), Eric Dier (Tottenham), Joe Gomez (Liverpool), Reece James (Chelsea), Michael Keane (Everton), Harry Maguire (Manchester United), Ainsley Maitland-Niles (Arsenal), Tyrone Mings (Aston Villa), Bukayo Saka (Arsenal), Kieran Trippier (Atletico Madrid), Kyle Walker (Manchester City)
Midfielders: Jordan Henderson (Liverpool), Jack Grealish (Aston Villa), Mason Mount (Chelsea), Kalvin Phillips (Leeds), Declan Rice (West Ham), James Ward-Prowse (Southampton), Harry Winks (Tottenham)
Forwards: *Tammy Abraham (Chelsea), Harvey Barnes (Leicester), Dominic Calvert-Lewin (Everton), Danny Ings (Southampton), Harry Kane (Tottenham), Marcus Rashford (Manchester United), *Jadon Sancho (Borussia Dortmund)
*not currently with squad