This week tax collectors go on a rolling three-day strike over the loss of another 5,000 staff. The Public and Commercial Services Union (PCS) says there is a backlog of letters unanswered and the public are “tearing their hair out” trying to get through on the phone, with the 281 frontline offices offering help and advice now closed.

These cuts look mind-blowingly self-defeating, as ARC, the union for HM Revenue and Customs managers, says investing £312m in staff raises £8bn in tax. PCS says 90% of tax is effectively voluntary, with so few staff to check suspect cases. The National Audit Office reports that HMRC has in one year doubled the amount of tax debt written off, partly due to its own errors. Perverse incentives encourage HMRC staff to write off cases just to get through the work.

It’s not just unions complaining about the stripping out of tax inspectors. I interviewed a senior partner in a respectable Sheffield accountancy firm who said closure of their local tax office means collecting less tax, through loss of crucial local knowledge. “You used to call a local inspector who knew us and the client. Now it’s a call centre somewhere and someone who has no idea what you are talking about. They say they’ll call back but they don’t. They tell you to write, they don’t reply.” Inspections are much rarer, he says.

In his interview on the Andrew Marr Show, Ed Miliband said Labour would go after corporate tax avoidance. High time, since a large hole in predicted tax receipts has opened up this year. Some is due to the loss of good jobs, substituted with low-paid ones. But slabs of corporate tax are vanishing, as Britain turns into a tax haven that cheats itself in the process.

Labour’s record on chasing tax loopholes was dismal. In 2009 it set up the patent box – a vast new tax avoidance vehicle. Supposed to entice entrepreneurs with a 10% tax rate on any patented product, all it brought was enterprising tax lawyers applying the 10% tax to anything that had even a tiny part with a patent inside it, not even manufactured in the UK.

This government’s new enormous tax escape hatch is the controlled foreign companies regime, allowing UK companies to pay tax in the cheapest country they can find, and none when they bring profits back. At the same time, corporation tax is falling from 30% in 2007 to 20%: as a tax haven, foreign companies set up here with an artificial tax HQ, but their real jobs and money stay away. How can Barclays get away with claiming most of its profits are made in Jersey and Luxembourg, where they have few staff?

Labour’s well-intentioned attempt to support the film industry with tax relief has ended up being taken advantage of. In my inbox this week came a lurid offer for the enterprise investment scheme: “Be part of the booming film industry”, expect “stellar returns”. How? “30% tax relief, no capital gains tax. No tax on profits. Exempt from inheritance tax. Fully approved by government.” The company is called Stealth Media Films, and despite criticism of some celebrities on this scheme, it is still legal.

The public tells pollsters that tax swindling matters most in their view when it comes to a company’s ethics. What public accounts committee chair Margaret Hodge started with her grand inquisitions of tax-avoiding corporations, taken up by UK Uncut protesters, has sparked deep public indignation. As the government obstructs international negotiations, tax cheating is an issue ripe for Labour to make its own. Better still is a harvest of very ripe fruit for picking in these cash-starved times.

Margaret Hodge is gunning for all tax reliefs. In the name of tax simplification, she would do away with them. Not counting the enormous pension tax reliefs or personal tax allowances, the treasury hands out £100bn a year in tax reliefs that are an accretion of past chancellors’ whims and pet projects, full of nonsensical anomalies. She cites a small one: cleaners, nurses and other night shift workers can’t claim against tax for their taxi fares to get home safely at night, but a lawyer, accountant or professional can.

Even reliefs designed with the best of intents, she says, are wrong-headed. Why did the chancellor give tax relief to provincial theatre in his last budget – an excellent cause – when he could have given the same sum to the Arts Council to distribute to them more rationally? Why give a fortune randomly to companies for R&D, when these huge gifts should awarded as well-considered grants through research councils? An attempt to pick winners is better than random scattering of funds when so much of it vanishes down greedy tax loopholes, doing no good. Why inflate house prices by giving tax relief on mortgages for buy-to-let landlords?

Transparency is her other demand. Public companies should be obliged to open their tax accounts, so everyone can see where tax is due instead of secret deals struck by the likes of Vodafone with HMRC. Hodge would ban any tax-avoiding company from government contracts. That might stun the big four accountancy firms, who she says earn £2bn a year in “tax advice” to companies, depleting the state while simultaneously earning handsomely from the government. Why are their advisers seconded to the Treasury to set up the schemes they will help others avoid?

Tax campaigner Richard Murphy has just published his latest assessment of the Treasury’s missing taxes – a gap he sets at £100bn. The difference between this and the Treasury’s £35bn estimate comes partly from Murphy’s recent uncovering of some 360,000 companies not declaring income, never checked by the staff-starved HMRC, with a sample of 40% of declarations found to be fraudulent. But most of all, he would change the law to assert a general avoidance principle, to stop rules being wriggled around, but let HMRC strike down any activity whose purpose is plainly to avoid tax.

Ask Murphy where money is to be had and he has large sums to offer. Start by bringing back the level playing field, abolished in the Thatcher era, between tax on earnings and investments. If the same 13% national insurance was charged on earned and unearned income, that would stop people setting up artificial companies just to avoid it – and it would bring in £40bn.

Hodge would confront Amazon and the rest right away. “Don’t wait for international negotiations. It will take forever; just close the loopholes now.” She has strong allies in making companies pay tax where they make profits. I asked Michael Heseltine recently what he would do, and he gave one of his leonine glares and said: “Go after them! How many gunboats has Amazon got?” Labour should follow Hodge and Heseltine’s advice. They need the money – and the public would cheer.

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