The Manchester United midfielder told the Football Association he did not want to be selected for Euro 2012.
However, he has now made himself available and comes into a squad that sees Tottenham duo Caulker and Livermore selected for the first time, in addition to Chelsea's Ryan Bertrand.
In total there are six players who could win their first cap for England, with midfielder Tom Cleverley and goalkeepers Jack Butland and John Ruddy also hoping to make an appearance having previously been named in squads but not taken the field.
England captain Steven Gerrard, plus established regulars John Terry, Wayne Rooney and Ashley Cole, were left out of the squad for Wednesday's match in Berne but Frank Lampard - who missed Euro 2012 through injury - has been included.
Only 10 players remain from the squad that made the quarter-finals of Euro 2012.
England start their qualification campaign for the 2014 World Cup in Brazil against Moldova on September 7.
Goalkeepers: Jack Butland (Birmingham City), Joe Hart (Manchester City), John Ruddy (Norwich City)
Defenders: Leighton Baines (Everton), Ryan Bertrand (Chelsea), Gary Cahill (Chelsea), Steven Caulker (Tottenham Hotspur), Phil Jagielka (Everton), Kyle Walker (Tottenham Hotspur).
Midfielders: Michael Carrick (Manchester United), Tom Cleverley (Manchester United), Frank Lampard (Chelsea), Adam Johnson (Manchester City), Jake Livermore (Tottenham Hotspur), James Milner (Manchester City), Alex Oxlade-Chamberlain (Arsenal), Jack Rodwell (Everton), Ashley Young (Manchester United).
Forwards: Andy Carroll (Liverpool), Jermain Defoe (Tottenham Hotspur), Daniel Sturridge (Chelsea), Theo Walcott (Arsenal).
- John Ruddy
- Jack Butland
- Tottenham Hotspur
- Manchester City