John Dunford has written to the education secretary calling for an overhaul of specialist status

But the head teachers' union says the proposed expansion of this scheme to about a quarter of secondary schools threatens to create a "two-tier system".

The government says that exam results in specialist schools have improved more quickly than in other types of comprehensive - and that it wants to replicate this pattern of success.

Selection

But the Secondary Heads Association says that the improvement in results reflects the improved funding - and that all schools should be able to receive a similar level of funding.

A specialist school, St Marylebone in Westminster, was the most improved this year

Such diversity of funding was at odds with the government's ambitions for equality of opportunity, said Mr Dunford.

Instead the union says that all schools should be able to apply for specialist status - and that there should be no areas of the country where specialist status is not available.

And as a way of speeding up the process of spreading specialist status more widely, the union proposes halving the extra funding per school and doubling the numbers participating in the scheme.

In his letter to the education secretary, Mr Dunford also proposes the removal of specialist schools' right to select 10% of pupils and calls for the widening of the categories of specialisms.

But the government points to the success of specialist schools and says that it will be easier for schools to apply for specialist status in areas where specialist schools already exist.

"A temporary ceiling on the new designation of specialist schools in areas with large numbers of those schools will be lifted and additional resources made available," said a government spokesperson.

"But the objective of that restriction was to help schools in the most challenging areas and to secure a balanced and fair distribution of specialist provision."