There is a particular problem with small schools because they offer lower salaries to heads and demand greater teaching commitment.

John Rose, Somerset’s education director, says: “In the mid-1990s, for even the smallest schools you got long lists and short lists that offered genuine choice. I am not saying you don’t get good candidates now, but there are clearly fewer of them.”

Higher-than-average house prices are forcing out local families who are replaced by young professionals who delay having children, exacerbating falling rolls.

Mr Rose said younger staff also seemed less attracted to country life, with more wanting urban experience.

When village schools do find heads, they are likely to move after five years or fewer, against the eight to 12 years heads stay in larger schools.

The county has nine schools with 30 pupils or fewer and, rather than close them, it has appointed heads to oversee more than one school.

The first such arrangement began in September between Crowcombe and Stogumber, two C of E village first schools four miles apart, with 31 and 24 pupils respectively.

Anthea Deane had been Crowcombe’s head since 2000 and, for a small pay rise, she took on Stogumber. This has led to longer hours, but this should improve next term when the two governing bodies merge to create a full federation, cutting out much duplicate work.

It will also allow more flexibility, with teachers moving between sites. Ms Deane said: “It has meant more work but I do see it as worthwhile because I wanted to ensure these two schools continued to serve their communities. I don’t know what the alternative would have been but I don’t think it would have been a happy time.” WS