UEFA spokesman William Gaillard said: "You can't call up another player after the tournament has kicked off. We are sorry."
The only exception to the strict rule was made at Euro 96 when Germany were allowed to call up a player because they were suffering with an unusually large number of injuries in the later stages of the competition.
Sven-Goran Eriksson is well covered in midfield, with Owen Hargreaves, Kieron Dyer, Phil Neville and Joe Cole all available. This would tend to back up UEFA's view.
Against Switzerland on Thursday, Hargreaves looks the favourite to replace Paul Scholes, who is a major doubt after twisting his ankle.
There were a number of absentees from training today including captain David Beckham, Sol Campbell and Steven Gerrard, who were all suffering from blisters. Gary Neville also missed the session with a slight calf strain.
The Swiss have been allowed to call up a new goalkeeper, Sebastien Roth, to replace the injured Fabrice Borer in their squad.
As goalkeepers are a specialist position, UEFA regard this as an "exceptional circumstance".
