Last week saw a major payday lender go bust, a significant British company, Costa, sold overseas for short-term reasons and executive salaries continuing to soar. Yet a disproportionate amount of public hand-wringing will be directed at Crossrail, now deferring its opening by a year while over-running its budget – further proof of the endemic inability of the British public sector to do anything well (in contrast with the ineluctable efficiency of Britain’s private sector).

Let’s sing a different tune. Therailway line, more than 60 miles long, linking Reading and Heathrow in the west to Shenfield and Abbey Wood in the east – adding 10% to London’s commuter rail capacity – and set to carry around 200 million passengers a year, will be a fantastic achievement. Its 13-mile-long tunnels run more than 100ft under the capital’s streets, navigating everything from underground sewers to the deep foundations of skyscrapers with superb engineering aplomb. The longstanding reproach is that Britain can’t do grand projects. Crossrail, now christened the Elizabeth line, is proof that we can.

Except praise has to be qualified by recognition of problems of performance, incentives, expense and governance exposed last week. They do need to be addressed, but only to make sure our engineers can continue to express their daring. For all his talent, Crossrail’s former chief executive, Andrew Wolstenholme, should not have been allowed to leave six months ago with a multi-hundred-thousand-pound performance bonus when there must have been warnings that looming problems with signalling, safety and train deliveries would make a delay in opening almost certain. This was reward for failure.

Too many subcontractors in the supply chain see a golden opportunity to fleece the state

And although the cost overrun is small– 4% – it comes after Wolstenholme and his then board were predicting a £500m cost underrun. Now the contingency in the £16bn budget has been eaten up, raising the baseline for costs for the next big infrastructure projects, and giving the Treasury’s infrastructure sceptics precisely the ammunition they need to kill them. Suddenly, a success story is being transmuted into a story of incompetence and greed, presided over by Chris Grayling, our least competent transport secretary for a generation, still in office solely because the political balance in cabinet requires a Brexiter. (Being a Brexiter, the country is learning, is synonymous with incompetence and bad judgment.) Yet even Crossrail’s critics do not contest its necessity. It should be the precursor of a wave of new infrastructure projects that are so badly needed around the country. The National Infrastructure Commission has identified a dozen vital projects blighted by Britain’s approach to investment. These include HS2 and Northern Powerhouse Rail (the latter, previously called HS3, links major northern cities from Liverpool to Newcastle to Hull), Crossrail 2 (linking north-east, central and south-west London), eastern crossings of the Thames, Heathrow’s third runway, Hinkley Point C, 5G mobile and the water and flood defence infrastructure.

Most of these are not happening or, in the case of Crossrail 2 and Northern Powerhouse Rail, only stumbling along. If Crossrail can be tarred sufficiently as an exemplar of bad management inherent in the way the public sector does things, then the stumble will turn into cancellations. Be sure Crossrail 2 will be subjected to yet another review. Northern Powerhouse Rail, vital to the future of the north, hangs in the balance. The open question is how should Crossrail, and Britain’s infrastructure performance generally, be benchmarked? Compared with the collapse of Carillion, in January, it represents efficiency and high-quality custodianship of other people’s money. Wolstenholme’s performance bonus was unjustified – it should have been awarded only when the line was up and running – but it would raise few eyebrows when measured by the criteria set for many executive sweeteners in the private sector.

Britain’s management culture has become corrupted by too much pay for too little: a generation of private sector managers skilled at becoming short-term value extractors to support the immediate share price is not much good at creating value in big infrastructure projects. Too many subcontractors in the supply chain see a golden opportunity to fleece the state. It is often unsung and poorly paid officials who pull projects through.

It is when gauging Britain’s efforts against Germany or France that the real shortcomings are exposed. French construction costs in rail are up to half our own. They do not insist on the same myriadcompanies, with contracts sliced and diced in the name of contestability, making projects unmanageable. Nor do they organise a procurement system in which contractors bid low to secure the bid and then raise their costs, knowing it is too expensive to sack them. In France, single contractors, managed by officials, bid to manage the contract against closely benchmarked costs.

Nor are the benefits of, say, a new high-speed rail line on property values and uplift in local economic activity left untaxed, as they are in the UK. New Labour, initiating Crossrail, did successfully insist on a levy and a supplementary contribution from the business rate. But there has been no attempt to secure any wider tax benefit from the boost in property values that were certain to follow – and which dwarf the cost over-runs.

But this cuts little ice with Grayling, an anti-statist, anti-tax, scrap regulations ideologue. In thrall to the notion that the private sector is superior, he is constantly surprised by contractors failing to deliver and rampant mismanagement. Yet Britain desperately needs a wave of new infrastructure. Cheap and plentiful finance is abundant. What is lacking is the willingness to access it and the accompanying management and state capacity. This has been weakened by self-damaging cuts in civil service numbers, skills and pay. This was not the EU’s doing. We did it all by ourselves – and reversing it is what we should be discussing.

• Will Hutton is an Observer columnist