The Education Secretary dropped in on Frosterley community primary, County Durham, where his grandfather had been head, when Michael Sharland berated him about the hours he has to teach to balance the budget.
Mr Sharland, who has been head of the small village school for 22 years, told The TES that he has to teach for 80 per cent of the school day.
He said: "There simply aren't enough hours in the day for me to read the documentation on the new regulations coming in, or go on the necessary courses."
He added: "We had a successful inspection in 2002, but we've lost our way somewhat over the past year or two. A lot of work was done several years ago so we have lessons in place, but there's no time to review them."
Mr Clarke's grandfather, William J Skinner, was head of the school between 1919 and 1952. His mother, Brenda, was a pupil.
Mr Sharland said Mr Clarke acknowledged the problem of heads' teaching burden during last month's visit. The Department for Education and Skills said April's school budget plans would ensure councils pass cash to schools in full. Heads would be trained to balance their budgets.