In their joint submission to the School Teachers' Pay Review Body, they describe cash grants to new maths and science teachers as an ineffective attempt to solve the problem "on the cheap".
They do not name a figure for the pay rise, but argue that a substantial sum is needed to recruit and retain enough teachers to deliver Labour's ambitious class size and performance targets.
Meanwhile - in a separate statement - headteachers say they will not co operate with the Government's Green Paper pay reforms unless their pay is on a par with similar jobs in industry.
The National Association of Head Teachers argues that up to pound;1.5 million is needed next year to compensate for a pay shortfall of 12 per cent.
This is the second year that all the heads' and teachers' unions have united to present a joint submission to the pay review body on top of their individual proposals.
It concentrates on recruitment and retention, highlighting the problems of an ageing profession and of recruiting male teachers.
Only 32.7 per cent of teachers in all maintained schools are men, compared with more than 35 per cent in 1992. Only 17 per cent of teachers are in their twenties, with two-thirds over 40.
Teachers' salaries and pay progression have continued to deteriorate relative to other graduate occupations, the unions argue. The average starting salary for graduates is pound;17,400 compared to pound;15,537 for teachers. On average, graduate salaries climb by more than 40 per cent in three years compared to only 18 per cent for teachers, or 25 per cent for those with extra responsibilities.
Their submission says that the Government's targeted incentives such as bursaries for new maths and science teachers is an "ineffective attempt to address teacher shortages on the cheap" that will have a limited effect long-term.
Seven of the 11 main secondary subjects are now officially designated as suffering staff shortages. Union officers say the fact that only art, English, history and physical education are not designated as shortage subjects shows the widespread teacher supply crisis in secondary schools.
In their individual submission, the National Union of Teachers argues that conditions of service should not require staff to teach a class or more than 30 pupils, or to cover for absent colleagues for more than one day not arranged in advance.
The NUT also proposes that teachers should spend at least a fifth of the school week out of the classroom.
David Hart, NAHT general secretary, said: "Heads are prepared to adopt a constructive approach to the fundamental changes in the Green Paper, but they are not willing to undertake their absolutely key role, in the delivery of the radical changes to the profession, unless additional responsibilities are recompensed in pay terms."