When was asked for examples, he reportedly said: "RWC 2003. England used faked blood (did not know whether capsule or cut by someone in medical team to manage replacements)."
The 55-year-old Richards, who played 48 tests for England, said he had been informed by someone from within the 2003 England squad.
Richards was director of rugby at Harlequins when team officials cheated in order to get former All Black Nick Evans back onto the field as a blood replacement, in order to use his goalkicking prowess.
It involved cutting the mouth of wing Tom Williams and using a fake blood capsule from a joke shop during the European game against Leinster. Harlequins used the ploy on other occasions.
George Robson, who played for Harlequins in that game, told talkSPORT he came off with a fake blood injury against Leicester.
"I acted as a blood substitute, having a piece of gauze with some blood on it on my head," the former lock said.
"That wasn't my blood, I don't know if it was blood, I presume it wasn't."
"My understanding was, this is the protocol, and the rationale is that it's going to help us win a rugby game.
"I didn't see anything wrong with that. I didn't think this is crazy or ridiculous and, 10 years on when I speak to people I work with or study with and share some of that insight, they look at me as if I've got three heads."
Woodward said Richards' claim about the World Cup team was "absolute nonsense".
"This is simply not true. I am not sure why Dean raised this. I have never been involved in anything like this. It is ridiculous."