The government currently pays £5.9bn to local authorities through its "high needs block" funding, which is then allocated to schools to support children with complex needs.
Heightened pressures include a 21 per cent increase between 2014 and 2017 in the number of pupils with statements of SEN or education, health and care (EHC) plans.
Between 2016 and 2017 alone the number of pupils with an EHC plan or statement rose by 31,000, NAHT said.
The cost of support is also rising due to an increase in the number of SEND pupils moving to more expensive, specialist settings. There has been a 19 per cent rise in the number of pupils with SEND attending independent special schools between 2010 and 2017.
"NAHT's analysis provides clear evidence that there is both increased pressure on the costs per pupil and increased demand for support for children and young people with the most complex special educational needs," said NAHT.
"The Chancellor must recognise the growing shortfall if we are to avoid our most vulnerable pupils missing out on the education that can allow them to realise their potential."
The high needs funding block is used to provide special school places, support in mainstream schools as well as alternative provision for pupils with challenging behaviour, such as through pupil referral units.
It can also be used by councils to top up funding for SEND pupils but the Local Government Association (LGA) is concerned that a new funding formula for schools will make it more difficult for councils to do this.
Last month, the LGA called on the government to launch a "fundamental review" of high needs funding to ensure councils can meet the needs of children with complex needs.
A Department for Education spokeswoman said: "The high needs budget for pupils with complex special educational needs is £6 billion this year - the highest it's ever been - and core school funding will rise to a record £43.5 billion by 2020 - a 50 per cent real terms per pupil increase from 2000."