There have also been reports of a training pitch row between Danny Cipriani and attack coach Mike Catt the day before the 31-man squad was announced, with the players supposedly backing Cipriani.
That is rumoured to be behind claims by former captain Will Carling that Lancaster had run a "classroom-orientated environment" and treats players like "schoolboys".
There have been other claims from some sources in the camp that players are frustrated over restrictions on attending social events.
The perceived preferential treatment of Burgess, lured from Australian league on a contract said to be worth more than $NZ1 million a year, and the disquiet over the influence of Farrell in selection decisions is only further ramping up pressure on Lancaster holding his job.
His future will be determined by a post-tournament review led by (England) RFU chief executive Ian Ritchie, although it is possible that the head coach will resign ahead of that process. Ritchie's hold on his job, meanwhile, could be threatened by a special general meeting to call for a vote of no confidence in the board.
Ritchie accepted on Sunday that "change in the broadest sense" was now inevitable in the wake of the 33-13 defeat by Australia at Twickenham on Saturday night but insisted that there would be no knee-jerk reaction.
The details and timeframe of the World Cup review have yet to be confirmed but it will contain confidential feedback from members of the squad as was the case in 2011 when their evidence ended up being leaked. Interviews are likely to reveal a significant level of discontentment at England's preparations.
Lancaster and Ritchie fronted up at a press conference overnight when the head coach appeared resigned to his fate.
"I don't think I'll ever come to terms with this, personally, because it was such a big thing," Lancaster said. "As a coach, I've had some great moments coaching England and I've had some disappointing ones but this pales everything else into insignificance because of what the tournament means to everyone. This is going to sit with us all forever.
"That'll be the overriding emotion I'll have for a long time I think. I need some time, obviously Ian needs some time and the RFU does as well. I think we'll make the right decision at the right time."
But the fury at England's exit, their worst performance in the history of the World Cup and the first time a host has not reached the knock-out stages, has also put Ritchie's own position in the spotlight.
Before the tournament Ritchie, who came under fire last year for handing Lancaster and his coaching team six-year extensions to their contracts, had insisted that the responsibility for England's performance at the World Cup would lie at his door.
The British Telegraph reported it understood that a number of clubs across the country are confident they have enough support to call for a special general meeting to call for a vote of no confidence in the board unless there is significant change to the management of the governing body.
Asked if his future was intertwined with that of Lancaster given that he had appointed him as head coach and agreed his contract extension to 2020, Ritchie added: "The key thing about responsibility in my view is when times are difficult and when there are challenges ahead.
It is understood that the contracts of Lancaster, who is thought to be on £400,000 ($NZ942,000) per year, and his coaching team are rolling, so any dismissals would only involve a redundancy payment of a year's salary but that could still cost the RFU over £1 million ($NZ2.35m).
England, in the first instance, are likely to receive a sanction from World Rugby for failing to make 10 players available to the media after the match on Saturday night as part of the tournament regulations.
Former English winger Mark Cueto said Lancaster's position was now untenable.
"When he came in, he had some pretty strong words to say about the 2011 regime - one that I was part of - and our pride in wearing the shirt and so on," Cueto wrote in his ESPN column. "I still take that very personally. We won all our group games, and went out to a side who made the World Cup final . His team have lost two games out of three in the pool and are out with a game to spare. He's got to go."
But Lancaster is hoping that player feedback will be supportive of him.
"Clearly, I have invested a lot of time in one-to-one relationships with the players and I'd like to think I've got an open door where people can come in and tell me any problems and issues that arise," Lancaster added. "I've got a leadership group. I think it's only right that the players do give their feedback . Players' views are always sought. I would like to think they would be supportive but obviously it would be up to them to give their opinion."
