Earlier this month work and pensions secretary Iain Duncan Smith and chancellor George Osborne claimed their changes to our welfare system mean, "no longer will it be possible to be better off on benefits than in work". The prime minister wrote the same in the Sun, calling it a "crazy situation".

The government's line, as it very gradually rolls out Universal Credit from today, that it is "making work pay" has cross-party support. "We would make work pay," promises Duncan Smith's mini-me Liam Byrne, while shadow chancellor Ed Balls affirms that "it must pay more to be in work than live on benefits."

My union's members, tens of thousands of whom work on the benefits and tax credits system, are confused. A jobcentre worker told me: "All the calculators that we use in jobcentres are designed to show that you would be better off in work."

So if politicians are telling us all that you can be better off on benefits, and jobcentre advisers are telling claimants that they would be better off in work, someone is being lied to. But who? Iain Duncan Smith should come clean. But not being one to look for pots of gold at the end of rainbows, I asked my union researchers to look into it.

They found the DWP’s "tax benefit model" – data which showed how much better off people out of work, in a range of circumstances, would be by moving into employment. Publication of this data was, intriguingly, abandoned in 2010 – just after the coalition government was elected, but a similar calculator is still used by DWP staff. It shows what would happen if someone moves into work for 30 hours per week. Even on the minimum wage, the legal minimum, benefits only deliver 79 per cent of what you would be paid in work.

We looked again to see if the same was true for only 16 hours of work – after all there are 1.4 million people working part time because they can’t find full-time work. This time benefits were only worth 81 per cent of a working income. Jobcentre advisers tell me these figures closely match the ones they use today.

For verification, we checked against data collected by the Organisation for Economic Co-operation and Development on all major countries’ welfare systems, including the UK’s. Like the DWP calculator, it factors in housing costs and benefits, and it assesses what is called the "replacement rate" for moving from benefits into work for 30 different household types – and in not one single case would a household be better off on benefits.

It does not feature in either the DWP's or OECD's models, but work might not pay for those who work very few hours in low paid jobs. But the irony here is that Duncan Smith has himself actually made this more likely by increasing the number of hours people need to work before they receive working tax credits.

The "better off on benefits" fallacy has become common. In truth, there has always been a clue that it is an urban myth: no one who claims it exists has ever actually given up work to live the benefits high life. And why not? Probably because deep down they do not believe it, but it is also true that even when the benefit of working is highly marginal, most people want to work. As unemployment climbs above 2.5 million, and 6.8 million counting as underemployed, the reality is there are fewer than half a million job vacancies. The real issue for the government is not making work pay, but making work exist.

PCS members working in jobcentres face a bullying management driving down their own living standards and setting targets that staff are told to deny exist. Low pay is so endemic that up to 40 per cent of the DWP’s own staff will be eligible for Universal Credit themselves. It is grim, far worse than when I started working for the DHSS in the early 1980s. Back then we helped claimants and took as long as was necessary to get them the benefits to which they were entitled.

On the other side of the counter (or more likely now on the other end of a phone) it is even worse, with claimants subject to more and harsher sanctions, unprecedented demonisation from ministers and a Pavlovian press trained to foam at the mouth at the mention of scroungers and skivers.

As well as challenging ministers’ myths, we have a duty to challenge their hatred-inciting rhetoric. So the next time Iain Duncan Smith – or anyone else for that matter – claims people are better off on benefits, hand him a pen and paper and ask him to show you how.

Mark Serwotka is the General Secretary of the Public and Commercial Services Union