The tourists have sent a Level 3 charge - one which brings with it a ban of up to four Tests, if proven - over Anderson's altercation with all-rounder Ravindra Jadeja as the teams made their way off for lunch on day two of the first match in the series at Trent Bridge.
Subsequently, as the ECB had promised, the home team's manager Phil Neale sent a Level 2 counter-allegation against Jadeja.
Cook, preparing for the start of the second Test at Lord's, acknowledges exemplary standards of behaviour are non-negotiable for his team.
But he will not be asking Anderson to tone down his aggression on the field, because he believes that is when England's linchpin seam-and-swing bowler is at his best.
"No, I don't think I will," said Cook.
"We have a responsibility, as England players, never to cross that line. In the heat of the battle, when the emotion is up, there have probably been situations throughout everyone's careers when they've probably looked back and thought, 'I wish I hadn't done that'.
"I don't think this is a case (like that)."
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Accordingly, he will be telling Anderson to change nothing.
"I like it when Jimmy's in that battle, because I know he's up for it and desperate to do well for England," said the captain.
"When people are watching that, I think they get behind it and see a very competitive guy. I think people enjoy it."
James Anderson, left, and Ravindra Jadeja, batting, are involved in a conduct row
Cook had other issues to ponder in readiness for a match in which England will be out to end a sorry sequence of nine Tests without a victory.
Left-arm spinner Simon Kerrigan's chances of joining the effort appeared restricted by a pitch with plenty of grass cover and more likely, certainly than Trent Bridge did, to favour the seamers.
Kerrigan suffered a miserable debut against Australia last August, and Cook said: "I think it will be a big challenge for him, in terms of what he experienced in his first Test match.
"You obviously want to hit the ground running and show everyone what a good player you are, and you've always got to prove that when you first get into a side.
"Obviously, he has a little bit of a hurdle to get over. But from what I've seen in the nets, and talking to him, he certainly feels more comfortable around this squad (than he did last time).
"I think at some stage (in this series), we will definitely need a specialist spinner.
"We know that and it is a case of getting Simon in and around as well.
"Obviously (after) what happened in his first Test match, he needed a bit more time around the environment rather than just throwing him."
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