It’s not just high-profile tax avoiders like Jimmy Carr who are in the government’s firing line now.

According to Treasury minister David Gauke, it is “morally wrong” for ordinary people to pay tradesmen cash in the knowledge that the money isn’t going to show up in their accounts.

He told the Daily Telegraph: “It is illegal for the plumber but it is pretty implicit in those circumstances that there is a reason why there is a discount for cash.

“That is a large part of the hidden economy.” Really?

How much tax is being lost through “off the books” deals?

The figure being bandied about almost everywhere today is £2bn, but as so often when big scary numbers dominate the headlines, when you peel away the layers of the onion, there’s nothing in the middle.

That number comes from this 2008 House of Commons Public Accounts Committee report, but it’s worth quoting the figure in its original context: “There are no reliable estimates of the tax lost through the hidden economy. But it could be over £2bn and involve around 2 million people.”

That’s about as vague as it gets and, in any event, that estimate doesn’t relate specifically to tradesmen evading some VAT by getting paid in cash.

The £2bn is based on what HMRC calls the “hidden economy”, a broad category of misbehaviour that includes businesses that are not VAT-registered at all as well as “ghosts” and “moonlighters” – workers who avoid paying tax on some or all of their earnings.

HMRC distanced themselves from the £2bn number and told us: “We do not have a separate estimate of the tax gaps that results from people paying in cash.”

The department told us that cash-in-hand culture will account for some of the £4bn it estimates was lost to the “hidden economy” in 2009/10, and it will also form part of the estimate the taxman makes for “tax evasion” – also around £4bn. How much of it? We don’t know.

Are the taxman’s numbers reliable?

HMRC says the total “tax gap” for 2009/10 – the total money lost to fraud, error, evasion, avoidance, you name it – was £35bn. But some critics have put the real figure much higher.

The Tax Justice Network campaign group thinks Britain’s real tax gap is at least twice as much.

They base that on estimates of the size of the “shadow economy” as defined by the economists who produced this paper for the World Bank – where the business is legal but there is an attempt to dodge tax, social security payments and other requirements.

Co-author Dr Friedrich Schneider, probably the world’s leading authority on the subject, said Britain’s shadow economy was worth 10.5 per cent of the country’s GDP last year.

If that’s true, it comes to some £164bn. A tax burden of around 37 per cent means the state has missed out on around £61bn, on a back-of-envelope calculation.

Does cash-in-hand really hurt the economy?

A tricky one, this. What the government isn’t saying today is something many economists agree on: a black market in services produces benefits to the economy as well as costs.

How can this be? Well let’s say you agree to pay your plumber £500 cash for some work, and he doesn’t declare it.

Even if the transaction is illegal he will probably spend the money in the shops, stimulating the wider economy and contributing indirectly to tax income through VAT on purchased goods.

One study carried out by Dr Schneider in Germany found that about two-thirds of money made in the shadow economy is spent in the official economy, and more than two-thirds of the services offered on the black market would disappear if they were forced to go overground.

What’s the bigger picture?

Our shadow economy, as defined by Dr Schneider, is significant but smaller as a percentage of GDP than most countries in the world.

The UK’s score of 10.5 per cent meant it was 27th out of 31 European countries in Dr Schneider’s latest study. Bulgaria was top with 32.3 per cent.

And the size of the UK’s shadow economy, while possibly growing slightly very recently, has consistently fallen over the decades. That pattern is also borne out by research done by two Turkish economists who came at the problem using a completely different methodology.

Even if cash-in-hand accounted for all the tax evasion that goes in the UK (which can’t be true), it would still be less than the money lost to the Exchequer through what HMRC calls “tax avoidance” and “legal interpretation”.

Tax avoidance, not to be confused with evasion, is the legal, if morally dubious, exploitation of loopholes in the law. “Legal interpretation” is the taxman’s estimate of the avoidance that he doesn’t know about yet. Both are said to cost the state £5bn a year each.

Can you be prosecuted for paying cash?

If you’re the customer, it’s very unlikely.

An HMRC spokesman told us: “There is no law against paying someone in cash (or indeed asking to be paid in cash) and in many instances, whilst customers might suspect that by seeking payment in cash the trader is laying the ground for tax evasion, traders are not as blatant as to refer directly to tax evasion.

“But even if they do, the obligations are all on the trader, though we when we start an enquiry into the traders tax affairs we could approach the customer and ask how much and in what way the work was paid for.”

By Patrick Worrall