Metropolitan Police Commissioner Cressida Dick said it was determined that such action would not be in the public interest and the events took place too long ago for there to be sufficient evidence.
Michael Gove’s campaign was derailed by his admission that he took cocaine on a number of occasions when he was a journalist in the 1990s.
Boris Johnson, who is the favourite to beat Jeremy Hunt and become Britain’s next prime minister, said he thought he had been offered the drug once, although he sneezed so that it did not go up his nose.
Ms Dick told LBC Radio: “We have had a very quick look at all the things that have been in the public domain.
“You have to satisfy two things.
“Firstly is there evidence and secondly, the CPS would have to decide would it be in the public interest to take any action.
“Of course with things being so historic, it’s almost certainly not in the public interest but actually in the cases that we have read about, and I’m not talking about any of them specifically, but in all those cases there is no sign that there would be sufficient evidence.”
Ms Dick said she had looked at the information available and considered the admissions on the basis of law and Crown Prosecution Service advice given in previous cases.
“I looked at it myself,” she said.
“I just said to my team, somebody’s going to ask me the exact question. I think I know the answer but let’s just double check.
“The answer is on the basis of what we know, on what we’ve seen, there is no sign whatsoever that there would be sufficient evidence to take somebody to court, so we won’t be doing any investigating.”
Ms Dick was also asked about a row involving Mr Johnson and his partner last week that saw police called to the flat they share.
A neighbour called police amid concerns over the incident, as well as making a recording of it and passing it to The Guardian newspaper.
“I think it is important that people call the police when they’re worried about somebody, of course. That’s as far as it goes,” Ms Dick said.
“I’m a police officer and we ask people to tell us if they’re worried about somebody.
“It can be helpful for us if there is evidence of a crime, of course, that we’re then going to be investigating, if somebody has made some sort of recording that can be very helpful.”
But Ms Dick said that in a situation where both parties were fine and no crime had been committed, police would not have released the recording to the media.
“In an incident where we have been called because somebody is worried about somebody else, and when we get there both parties are fine and there are no offences, we would not put that into the public domain,” she said.