Under fire about funding, he said: “Whatever level of budget we have, if it was twice as big or half as big, the question still arises how do you get best value out if it.

“One of your jobs as heads is to manage it. One of my jobs is to make that easier for you.”

Mr Clarke’s speech at the new headteachers’ annual conference in London focused on personalised learning but he faced a barrage of questions about funding.

Gail Gregory, head of Sneyd community school in Walsall, accused him of fudging questions about cash.

She said her school had missed out on around pound;500,000 of leadership incentive grants because it was no longer categorised as in “challenging circumstances” after 30 per cent of pupils gained five good GCSE passes in 2002. The figure rose to 35 per cent this summer.

The school also stands outside an Excellence in Cities area.

“I respectfully suggest that my school has greater needs than the two independent schools and the city academy in that EiC area,” she said.

Kate Magiocco, head of Woodside infant and nursery school in Croydon, south London, said she had a “fantastic school improvement plan” that she was unable to implement because she expected budget deficits this year and next.

“I want to know how you can help me,” she said, to applause.

Mr Clarke said he and the Department for Education and Skills had made mistakes, and were working to ensure some certainty for schools about their future funding - for example, by agreeing a 29-month, rather than, a one-year pay deal for teachers.

Inevitably, if additional funding was targeted at schools with particular needs through initiatives such as EiC or leadership incentive grants, others nearby would miss out.

But to have no targeted resources at all would be wrong, he said.