This challenges the Government's view that the quality of the head is the most important factor in raising standards. Ministers have so far concentrated on the idea of creating highly-paid "superheads" as a way to improve a school's performance.
Margaret Hodge, chair of the Education Select Committee, said while the quality of the head was very important, it would be necessary to boost the role and status of classroom teachers if pupils' performance was to improve.
She said: "Heads are very important. But perhaps their most important job is to recruit the best staff they can for their school. Good quality teaching and collaboration between management and teachers is needed."
Last week MPs visited Zurich, where schools do not have heads. They found teachers there had high status, were well-paid and taught small classes. While the Swiss authorities are now proposing the appointment of headteachers, they admit it will result in larger class sizes.
Valerie Davey, Labour MP for Bristol West, said: "It was refreshing to see how the high status teachers have was reflected in their confidence. But the biggest lesson I learned was the importance of small class sizes."
Eamonn O'Kane, deputy general secretary of the National Association of Schoolmasters Union of Women Teachers, said: "The idea that the head is absolutely the crucial element is not borne out by reality. The head does do an important job, but British schools are still hung up by the public school idea of inspirational leaders in the Thomas Arnold mould."
He said school hierarchies should be broken down and teachers should be paid more for extra responsibilities.
David Hart, general secretary of the National Association of Head Teachers, said: "The select committee will put itself on a collision course with the Government if it rejects its headship model.
"But it is also futile to believe that heads can move mountains alone. We need a twin-track approach to improve the quality of leadership, and to invest into the crucial role of the teacher in the classroom."
The select committee report is due in the autumn. The MPs are still gathering evidence and will interview school standards minister Stephen Byers next month.
Nick St Aubyn, Conservative MP for Guildford, said: "We must still recognise the pivotal role of a head in a successful school."
The Zurich experience, page 4