The employers admit culpability: 30 per cent said the gaps were caused by their own failure to train staff, the same number said skills shortages damaged service to customers. Greater investment is urgently needed. But who pays? Almost 10,000 companies take no remedial action when vacancies arise due to skills shortages.

There is a terrible inertia throughout private and public sector businesses, relieved periodically by a swipe at schools and colleges - easy targets for blame. Meanwhile, statistics mount. One in five (135,000) job vacancies is the result of skills shortages.

Faced with these alarming figures, the Education Secretary Charles Clarke left no doubt where action was needed. “We are making an enormous contribution, but the public purse is absolutely not unlimited.” And there is no hope from the coming spending review. “We cannot imagine that big growth will come from the Exchequer.”

The answer is twofold: better use of existing funds and more from employers. He has given top priority to the needs of the 5m adults with basic numeracy and literacy problems. It takes no genius to see that many of the 2.4m “incompetents” are part of that 5m.

Beyond that, how well do the figures add up? Colleges train 3.5m adults but the Association of Colleges predicts that 70,000 courses for adults will close in the next two years because of cuts and shifting priorities.

The LSC survey offers some hope, with more employers than ever creating training plans. But if these are part of the wider pattern of collaboration with schools and colleges starting at 14, they will not bring lasting change.

A trawl through press and government archives reveals numerous false dawns for UK skills - witness those great skills white papers under trade and industry secretary Michael Heseltine in the late 1980s and early 1990s. The LSC has better evidence and more clout than funding bodies had then. But it still comes down to having the money to do the job.