Politicians should be drug-tested the minute they walk through the doors of Parliament, according to maverick independent senator Jacqui Lambie, who says people that believe the corridors of power are drug-free “are kidding themselves”.

Senator Lambie said she supported the Turnbull government’s plans to drug test 5000 new welfare recipients, but believed politicians should lead by example.

“These people up here are paid by the taxpayer as well,” she told Sky News.

“Start leading by example. I don’t see random drug-testing on that side of the house, or the Senate side of the house, when you walk in. Why can’t that be done?”

Earlier, the Tasmanian senator, who has spoken openly and emotionally about her son’s drug addiction, told the Seven Network: “If you think it’s drug-free up here, you’re kidding yourselves.”

Senator Lambie said Australia was well behind on drug rehabilitation, and the only point of the trial would be if people had full access to treatment and “a fair go to get back on their feet”.

Under the new budget measure, announced by Treasurer Scott Morrison on Tuesday night, those who test positive would be moved onto the Cashless Welfare Card and be referred for treatment.

.@JacquiLambie calls for random drug-testing at Parliament House. More: https://t.co/UI8GybsFY7 #Budget2017 pic.twitter.com/ZBYEumi3fU

— Sky News Australia (@SkyNewsAust) May 10, 2017

Independent senator Derryn Hinch, who also supported the proposal for welfare recipients, said he had no concerns about politicians being drug-tested.

Liberal MP Craig Laundy said he’d be “more than happy” to be drug-tested.

While Labor has not formed a position on the trial yet, the Greens have ruled out supporting it.

“If we’re going to start drug testing welfare recipients, how about we start with politicians and CEOs?” Greens Senator Sarah Hanson-Young wrote on Twitter.

The party’s leader, Richard Di Natale, said the trial would do more harm than good.

“I don’t think you deal with the problem of illicit drugs in the community by forcing people to get drug tested,” he said.

Senator Lambie suggested journalists working at Parliament should also be drug tested and called for random tests to be rolled out in other work places.

Asked about the drug-testing measure on Wednesday morning, Prime Minister Malcolm Turnbull said the lesson was “don’t do drugs”.

“The lesson is don’t do drugs and the bottom line is if you’re on welfare, what you’ve got to do is get off welfare and into a job,” he told the ABC.

“We’re doing everything we can to ensure we can achieve that. This is doing those people a big favour.”

Senate crossbench kingmaker Nick Xenophon said he was concerned by any measures that appeared “punitive”.

Senator Lambie, who has also spoken openly about her own struggles living on welfare, in April made an impassioned plea to the government to back away from welfare cuts.

“I want you to know that’s what it’s like to be at the bottom of the crap pile, through no fault of our own, for many of us,” Senator Lambie said in a speech that went viral.

“For you to take more money off those people, you have no idea how bloody tough it is. What you are doing is shameful.”