The home secretary has slapped down the government's drugs adviser for suggesting there must be more creative ways of dealing with personal drug possession than simply giving more people a criminal record.

Theresa May dismissed within two hours the call by Prof Les Iversen for much greater use of non-criminal penalties such as compulsory drugs awareness courses, assessments for treatment or confiscation of passports or driving licences.

Iversen's comments to the Commons home affairs select committee followed a recent submission by the advisory committee on the misuse of drugs (ACMD), which he chairs, to the Sentencing Council, arguing that those found possessing of drugs for personal use should not be processed through the criminal justice system but instead treated in a similar way to speeding drivers.

"There should be drugs awareness courses to which those found in possession can be referred as a diversion, which would be the equivalent of the successful speed awareness courses to which drivers can be referred," the ACMD said.

But May made clear that she was not interested in such an approach. "I have a very tough view on drugs. That view is informed by people I speak to who have seen the damage the drugs have done to people in their family," she said at a lunch for journalists at Westminster. "I think there are far too many people who think drugs is something you can do without it having an impact, but it does have an impact."

However, she said it was worth looking in more detail at Iversen's suggestion of a US-style Analogue Act that would ensure any new so-called legal high was banned as soon as it appeared on the market.

Prof David Nutt, Iversen's predecessor as ACMD chair, told the select committee that alcohol consumption could fall by as much as 25% if Dutch-style cannabis coffee shops were introduced into Britain.

He said the cost of policing cannabis use was £500m a year, mainly for issuing possession warning notices, compared with the £6bn a year bill for policing the use of alcohol, including dealing with people who were drunk and disorderly.

Nutt said he stood by his claim that horseriding was more dangerous than taking ecstasy, the comparison that triggered his sacking from the ACMD in 2009. He said the costs to the NHS of injuries of riders who had fallen from their horses were little realised, and nor was it appreciated that riders who lost control of their horses on the roads were the cause of more than 100 serious accidents a year.

"Horseriding is considerably more dangerous than taking ecstasy," he said. "It is a popular activity, dangerous but addictive. I am told that many riders find it difficult to give up."

Nutt said politics rather than science had dominated drug policy in Britain over the 40 years since the Misuse of Drugs Act was passed in 1971. Only one drug – cannabis – had been downgraded, and that was quickly reversed against the advice of the ACMD. He said the decision to classify magic mushrooms as a class A drug alongside heroin and crack cocaine was "the final nail in the rationality of the 1971 Drugs Act".

Nutt has suggested that the harmful impact of removing criminal sanctions on cannabis use would be relatively modest unless it was as actively marketed as alcohol, since almost half of young people already used the drug. He said he had argued in a Lancet paper that alcohol was the most harmful drug in Britain, largely because of its frightening contribution to domestic violence, child abuse and road accidents.

"A regulated market for illicit drugs would be the best way and we could reduce alcohol consumption by as much as 25% if we had the Dutch model of cannabis cafes," Nutt told the MPs, adding that he believed the police would rather deal with people who were stoned than drunk.

He said: "The drugs trade is the second biggest international trade in the world, after oil, and it is completely unregulated … It is impossible to win the war on drugs."

Tory MPs on the committee said the idea that horseriding and taking ecstasy were "morally equivalent" was irresponsible. Mario Dunn, Alan Johnson's special adviser who was involved in the decision to sack Nutt, said the comments proved that "no responsible government would have David Nutt as a drugs adviser".