Sadiq Khan has a plan. The mayor of London may not have made great strides to solve the capital’s housing crisis so far – but it is, he likes to remind people, a marathon not a sprint, and slowly his plan is coming into view. A draft of his long-awaited housing strategy, published today, outlines plans to spend £250m buying and preparing land for new affordable housing.

Fixing this problem, though, is going to be an expensive business – so earlier this week, Khan also outlined a nifty way of doubling his £3.5bn affordable housing fund at a stroke. The main tax that has grown fat off the capital’s increasingly silly house prices, after all, is the stamp duty paid when they change hands. Revenues from stamp duty stood at £1bn in 2008; by last year, they’d soared to £3.4bn.

Since there’s a correlation between the size of those revenues and the size of London’s housing crisis, it makes sense to use the former to tackle the latter. All the mayor needs to do is persuade the Treasury to hand control of that money to City Hall, and – oh dear, I think I’ve just spotted the flaw in this plan.

Devolving stamp duty receipts isn’t quite as radical a step as it may appear. Khan’s predecessor Boris Johnson proposed something similar, and although there has been some grumbling from Tories in the London assembly, the idea has cross-party support. The real political faultline on this issue is between London politicians, who want more money devolved, and the Treasury, which – regardless of who is in Downing Street or how the economy is doing – has consistently treated fiscal devolution with a mixture of scorn and fear.

Despite the lack of support from the chancellor, Philip Hammond, the problem with Khan’s idea is not that it’s unreasonable: if anything, it’s that it’s not radical enough. Housing, after all, is both London’s biggest crisis and its biggest cash cow. It doesn’t feel like it should be beyond the wit of man to balance the two.

But London is a British city – and British cities have none of the financial freedoms required to do much of anything. Cash-strapped councils are empowered to flog their land to developers to plug the yawning gaps in their budgets, which is great, unless you’re a tenant or a taxpayer. But levy their own taxes, issue their own bonds, make their own investments? Not a hope.

A century ago, government was largely a local affair

It wasn’t always thus. A century ago, government was largely a local affair, meaning that councils were left to solve their own problems and build the things their citizens needed. We’re still familiar with the idea of council housing and local authority schools, even if both have been on their way out for some time, but in its heyday municipal government did far more than that: running its own tram and trolleybus networks, dealing with its own water supplies, even producing its own power.

In the 70 years since the war, however, money and power has gradually drained away to Whitehall. Explanations abound as to why: the need to nationalise to avoid postcode lotteries; corruption and mismanagement in local government; the tendency by ministers of one party to see councils run by another as nothing more than the enemy within.

Whatever the reasons, though, the result is that Britain has become one of the most centralised countries in the developed world, a place where national government sees councils as little more than its branch offices. All that’s left of the glory days is palatial Victorian town halls, full of empty rooms where important decisions were once taken.

How we can solve this is not immediately clear. George Osborne promised to devolve control over business rates with one hand, while snatching away government grants with the other. All this was supposed to encourage councils to attract more businesses in search of the money they’d bring with them, but in a country as divided as ours the inevitable result was that councils in rich areas got richer while those in poor ones fell off a cliff. Simply removing the subsidy from the system means that services will inevitably start to fail.

The same problem would apply to Khan’s stamp duty proposals, were they to be rolled out nationally. But that, really, is the point: the challenges faced, and solutions required, by different cities are too different for any one policy to fit all. In London, the problem is housing. In other cities, it’s often transport, facilities or skills.

There’s no easy fix for the funding gap – but the fact that transport investments in Bradford still have to win attention and approval from mandarins in Whitehall is self-evidently ridiculous. Sadiq Khan’s proposals to tackle London’s housing crisis may or may not work. But he was right about one thing: the Treasury needs to give up control.

• Jonn Elledge is the editor of the New Statesman’s cities site, CityMetric