Billy Twelvetrees is England's only outstanding injury concern heading into Saturday's first Test against New Zealand at Eden Park.
The Gloucester centre has been sidelined for one month with an ankle problem and will miss training again on Monday, although head coach Stuart Lancaster insists he remains in the frame for selection.
Hooker Rob Webber and prop Joe Marler are now expected to beat ankle and hip trouble to face the All Blacks in Auckland.
England will confirm their final New Zealand additions flying out on Monday, with Harlequins props Kyle Sinckler and Will Collier still locked in a "50-50" battle for the final berth.
"Billy still hasn't trained fully so we'll see how he progresses during the course of the week, but the clock is ticking now," Lancaster said.
"He's the major one - everyone else should be good to go."
Lancaster reported a clean bill of health on the Northampton and Saracens players involved in Saturday's Aviva Premiership final.
Number eight Billy Vunipola and fly-half Owen Farrell were suffering from cramp only and will reinforce the assault on the second and third Tests against the All Blacks when they arrive in New Zealand on Wednesday.
Lancaster was pleased with the performance of Northampton hooker Dylan Hartley, who completed his comeback from a shoulder injury as a second-half replacement in the 24-20 victory over Saracens.
"Dylan got on around 60 minutes and played the extra time as well," Lancaster said.
"He seemed to come through fine and he'll definitely be on the plane as he's an experienced player for us.
"As to whether Dylan will start the second Test, I'll make that decision after the first Test."
England's inexperienced and youthful XV slipped up 39-29 to a mighty Barbarians line-up at Twickenham on Sunday, former All Black Hosea Gear scoring twice.
Henry Slade impressed with a try and 15 points in total, with Dave Ewers and Charlie Sharples also crossing.
England XV head coach Jon Callard rated the Sinckler-Collier New Zealand tour duel as still "50-50" just hours from a final decision being made.
The RFU's player development head Joe Lydon admitted it would be tough to separate the duo.
"Given the volume of players that have travelled, there's one spot," Lydon said.
"Stuart has already been on the phone just to make sure everyone is all right.
"We'll have a conference call and discuss things; they have obviously seen the game.
"I'm confident they would stand up like they did today."