Burns has been called up to replace Harlequins centre Jordan Turner-Hall, who is suffering from an inflamed knee.
Twelvetrees also linked up with the England squad at Pennyhill Park on Sunday night to provide temporary injury cover for Jonathan Joseph, the London Irish centre who is carrying an ankle injury.
A total of 36 players were scheduled to convene on Sunday night, including Dylan Hartley and Courtney Lawes who will have their respective knee injuries assessed by the England medics.
England play Fiji at Twickenham on Saturday and then face Australia, South Africa and New Zealand in a challenging autumn campaign.
England head coach Stuart Lancaster said: "Freddie has been playing well in the Aviva Premiership and, with Jordan needing to stay at Harlequins for treatment, we are keen to have a look at him.
"JJ is continuing his recovery from an ankle injury and this is a good chance to get Billy in for training.
"As last week, George Robson and David Paice come in as an injury replacements for Courtney Lawes and Dylan Hartley. Both will be assessed and treated in camp and it is important that they stay with the squad as much as possible.
"We had a productive week at St George's Park and got a lot of work done. Now we are back at Pennyhill we will sharpen our focus towards Fiji on Saturday."
Burns, 22, is the leading points scorer in the Aviva Premiership with 124 and a fly-half who has a maverick touch but is also showing an increasing ability to manage a game.
World Cup-winner Will Greenwood is among those to have championed Burns' England credentials in recent weeks.
Twelvetrees, who joined Gloucester from Leicester in the summer, was described by Cherry and Whites director of rugby Nigel Davies as "almost the perfect 12".
The 23-year-old has been the ideal foil for Burns in Gloucester's strong start to the season.
The club that ended last year with six straight defeats are currently fourth in the Premiership with five wins and a draw from eight matches.
Lancaster will name his 23-man squad to play Fiji on Thursday.
At present Burns and Twelvetrees are providing injury cover and may have to wait for their Test bows, although Lancaster will see this as a valuable opportunity to give them a taste of the senior England set-up.
Toby Flood and Owen Farrell are Lancaster's leading fly-half options while Brad Barritt, Manu Tuilagi and Anthony Allen are competing for centre positions.
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