What is amazing about the banking crisis is how few officials and politicians – Vince Cable and, to a degree, City minister Lord Myners honourably excepted – have managed to express the rank unfairness of it all. Which is why last Tuesday evening's speech from Mervyn King, governor of the Bank of England, was so remarkable. Love him or loathe him – and it is hard to find anyone who loves him – he did give vent to some honest-to-God anger. It was good to hear.

He finally lost his rag and in an extraordinary speech struck the tone that the political class steadfastly avoids. The moral hazard of bankers making vast fortunes underwritten by ordinary taxpayers was perhaps the greatest of all time, he declared. Never has so much been owed by so few to so many, he opined, for so little reform.

He was scornful of trying to force bankers to use more capital to restrain their addiction to risky innovation and bonuses, a policy championed by Lord Turner, the chair of the Financial Services Authority, and the chancellor. It was certainly "worth a try", but the plain truth was that fleet of foot, endlessly inventive financiers would run rings around the PC Plods of financial regulation whether in London or Basel, where the international rules are agreed.

Then he launched an Exocet. If the status quo is untenable and unfair because it leaves us with banks so big they have to be bailed out in a crisis, and if the proposed increases in bank capital advanced by the government are unlikely to act as a restraint, then there is only one course of action left: we have to break up the megabanks. The speculative, risky parts of banks must be separated from the commercial parts which lend to business, consumers and home buyers.

This, after all, is what the Americans did after the 1929-33 crash. Under the famous Glass-Steagall Act, commercial banks were forbidden to offer any form of collateral, underwriting or loan that financed stocks and shares. The same could be done today. The banking the economy needs – so-called narrow banking – could be closely regulated and casino banking could be left to its separate, freewheeling devices.

The governor has had much bile poured over his head. King is accused of intellectual showing-off without any solid work to support his position and trying to embarrass the chair of the FSA who he knew was going to propose the opposite only a few days later. Which is exactly what Lord Turner did. Glass-Steagall is impossible in the current markets, he declared on Thursday, presenting the FSA's discussion paper. Universal banks that combine investment and commercial banking provide an important service to their business customers and are the rule in the US and Europe. You could not and should not stop them.

In any case, drawing the line between the casino and the rest in today's sophisticated financial world is impossible. The way forward, he repeated, is more capital, especially more capital for the casino parts of any bank's business. On top, banks should make "living wills", setting out how they would wind themselves up without any cost to the taxpayer. Together, that would hit them where it hurts.

So here are the two sharpest brains working in the official sector of British finance eyeball to eyeball. If the issue was some arcane aspect of accounting, it would hardly matter. But reforming big finance ranks alongside climate change and the Middle East conflict as one of the great policy challenges of our time. If the system continues unreformed, with megabanks reinventing the now dysfunctional casino, the next crash really will overwhelm us and the political fall-out could easily lead to protection and depression, alongside ugly nationalist ideologies.

As it is, the depth of recession and elusiveness of recovery are storm warnings. So who is right – King or Turner? Both make good points. King is surely right that the issue of banks that are too big to fail must be confronted. Relying on lowest common denominator international agreements on more capital and "living wills" can only go so far. So-called Basel 2, agreed in 2004, took years of horse trading and ended up embracing the approach to risk that brought the system down, in effect giving the big banks the green light to assess their own risks and capital needs.

This was the regime that allowed Northern Rock to pay a dividend the year it went bust and Lehman Brothers to borrow 50 times more than its capital. It hardly inspires confidence.

But Turner lands a counter-punch on the governor over doing a British Glass-Steagall. The US version unravelled over 20 years. In the Mervyn King-does-not-know-what-he-is-talking-about slide in his presentation, Turner asks rhetorically how Mr King thinks the separation between casino and commercial banking should be made. For example, customers legitimately want to hedge their positions in foreign currency and interest rates. Should they be forbidden to do it with their bank?

We should heed both men. Britain should now break up its banks that are too big to fail as the US once trust-busted Standard Oil in 1911 when it got far too large – the King solution. The impact on British finance and the powerful financial oligarchs would be irreversible and unforgettable. We could create more than a dozen banks where we now have four – NatWest, Bank of Scotland, and the Halifax should be given their independence again – and new banks created to specialise in infrastructure and innovation financing, where there is a gaping hole. There could be a genuinely competitive banking market, fighting to increase lending in all parts of the country and driving a sustained recovery. No single bank could pose a systemic risk because none would be large enough.

It would be a market, however, regulated and structured on Turner's principles. The more risky the banks' activities, the more capital they should be required to carry. Bankers' bonuses would be restrained by requiring remuneration to be linked to a far wider range of indicators that just the share price or the profit on a particular trading desk. Suddenly, we would have a banking system that serves business and customers alike and whose pay would come back to Earth.

The chairs of the megabanks will doubtless protest that the City's competitiveness will be irretrievably damaged – and London's mayor, Boris Johnson, will almost certainly harrumph with some typically rich Latin tags. There will be threats to leave, but to where? Singapore and Dubai do not have the GDP to underwrite trillion-pound megabanks and thus support markets deep enough to underpin their activities. British guarantees operate only in Britain.

In any case, the aim of policy after the biggest financial crisis for 60 years should not be to promote the City's interest and financiers' bonuses underwritten by the taxpayer. It should be to create a financial system that helps the economy grow and can stand on its own two feet. Breaking up big finance in a British Standard Oil moment would trigger sustained recovery. It would be hard not to vote for the party that had the steel to do it.