Labour leadership hopeful Andy Burnham provoked a minor storm on Cif last week with his proposal to introduce a land value tax (LVT). This was unsurprising – introducing LVT would be the most radical change to the tax system in a generation. But some of the comments need closer examination. This is a complex issue, and the benefits of a Burnham-style LVT are not immediately obvious. So what are the potential problems and benefits, how can they be overcome, and why abolish council tax, stamp duty and inheritance tax?

The case for abolishing council tax (CT) is easy. Council tax is an unfair tax that disproportionately hits the poor. A person living in a property worth £100,000 pays around 40% of the tax paid by someone owning a property worth £1m. This is palpably unjust. Taxation should be proportionate and based on the ability to pay. CT utterly fails these tests. We all know that the CT bands are a farce. Indeed, there has been no UK-wide revaluation since CT was introduced in 1991, because it is so unpopular, and politicians are well aware that average house values have more than trebled since then.

Stamp duty is also a regressive tax. It sets arbitrary bands – for example, if your house goes £1 over the £124,999 threshold you are immediately liable to pay £1,250, while hitting the £250,000 threshold subjects you to over £5,000 extra tax. It is a tax on transactions and, for young families and individuals without access to the Bank of Mum and Dad, a huge hurdle to getting on to the property ladder.

It is much fairer and more efficient to tax the value of land and property rather than transactions on it. Taxing transactions creates bubbles in the property market and leads to price volatility (as the crisis has shown us), something we should look to tackle in order to avoid a future property-based recession

The case for removing inheritance tax (IHT) is more difficult. Some who commented on Andy Burnham's article said they could not support abolishing a tax as morally justified as IHT. Back in June, I called for the coalition to increase IHT rates to 50% and to drop the threshold at which it starts to be paid. To me, inheritance is unearned income and I have always supported taxing it. But we (me included) have to face the facts that IHT is subject to massive avoidance, as the extremely rich have the means, and numerous methods, to avoid paying it. It only raises £3bn per year. What is the point in having a tax we can't police and which is so easy to dodge?

By contrast, LVT is impossible to avoid. Since it also proportionate – Mr Burnham's proposal would see the 130,000 households worth over £1m paying well over double their current annual CT bill – it hits the rich and would give those who struggle to pay penal CT bills, a sizable tax cut.

And don't forget that while LVT doesn't directly tax inherited estates, the inheritors would either pay capital gains tax if they sold the estate, or higher LVT if they held on to it. So for the rich, there is no way to avoid paying their share.

Of course, some comments rightly noted that forms of land taxation have been tried, unsuccessfully, since the second world war. But the key difference is that previous attempts were to get windfall gains from development projects on land. Burnham's proposal, it seems to me, is to have an annual levy regardless of the use of the land or development on it.

LVT has huge potential benefits for local councils. There are currently 700,000 vacant properties in the UK. Introducing LVT would be a massive incentive for local councils to make these properties fit to live in and find tenants and buyers, since otherwise they would be wasting millions of pounds. Moreover, it would also encourage businesses to locate in less prosperous regions, as the market value of land would be much lower than in prosperous regions.

Meanwhile, some worried about the effects of LVT on the "asset rich-cash poor", particularly pensioners. To me the solution is simple: a deferral system that means that inheritors pay the LVT on death, or family member(s) help pay the bills of their relatives.

While other leadership candidates have talked about wealth taxes and bank levies, Burnham is going many steps further. The beauty of LVT is its simplicity, efficiency and fairness. It could replace council tax, stamp duty and inheritance tax, and raise more revenue than all of them combined. It's an irresistible combination and Burnham's boldness is a sign that Labour is getting it right on tax again.