"Relentlessly reasonable" is an unusual rally cry - but this was no ordinary demonstration.

Hundreds of head teachers - the men in smart suits, the women in business wear - came to Westminster to make their point about school funding in England.

Ripples of applause filled Parliament Square - their meeting point and the scene of many a demonstration over the decades.

"Don't be chaining yourselves to the railings now ladies," someone joked.

It was clear that these protesters, passionate though they may be, would not have dreamt of it.

The gathering had more of an air of a collegiate conference than a demonstration.

"We're all a long way out of our comfort zone," one head teacher said.

"We asked each other on the bus if anyone had ever been to a protest before and nobody had," another added a little sheepishly.

The participants may have felt cheerful, and maybe little awkward, but the mood was nonetheless serious.

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One head teacher from Suffolk told how she had been bitten by a pupil this week.

"It wasn't his fault. It was because of a situation outside of school, and his emotional support had been cut two weeks earlier because of the cuts."

She could not give her name in case the pupil was identified, but she added: "We have children who are distressed and angry and we can't help them."

Another Suffolk head teacher, Kelly Head from Springfield Infants School, said: "It's head teachers here protesting because there's no one left.

"We are using people left, right and centre to cover all sorts of jobs in schools. There's no one left."

The organisers of this grassroots protest highlight Institute of Fiscal Studies' claim that per pupil funding has fallen 8% in real terms since 2010.

Their budgets have been squeezed by unfunded pay rises, national insurance payments, other cost pressures and rising pupil numbers.

'Heart-breaking decisions'

Others point to problems with England's new funding formula, which had been introduced to even out the amount which different local authorities receive per pupil.

Tony Markham, head teacher of Herne Junior School in Petersfield, Hampshire, told how his budget will be £250,000 in deficit by 2020-21.

The county has one of the lowest per pupil funding rates in the country, despite the new formula.

Ella Palmer, head of a school in Alton, Hampshire, said her school had been using money from its capital budget to fund laptops.

But these were now 14 years old, and the capital funding had been cut from £25,000 to £5,000 a year.

Another Hampshire head, Joe Ayres, said: "There just isn't enough money to do what we need to do."

Ms Head added: "It's heart-breaking because the decisions we are beginning to have to make are about reducing social care and mental health support."

The government insists school funds will rise to a record £43.5bn by 2020 and that a new funding formula is bringing bring more cash to schools.

National Association of Head Teachers (NAHT) leader Paul Whiteman said head teachers were not really "the marching type" and if they were protesting, something must be "seriously wrong".

This is the latest push in a campaign by school leaders to highlight the dangers of budget shortfalls and the different funding levels between schools.

Education Secretary Damian Hinds has recognised that funding is one of the biggest concerns in his brief.

A Department for Education spokesman said: "There is more money going into schools than ever before, rising to a record £43.5bn by 2020 - 50% more in real terms per pupil than in 2000.

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"Every school attracts more funding per pupil through the National Funding Formula, high needs funding has risen to over £6bn this year, and the 3.5% pay rise we announced for classroom teachers on the main pay range is backed by £508m government funding.

"We know that we are asking schools to do more, which is why we are helping them to reduce the £10bn spent each year on non-staffing costs, providing government-backed deals for things like printers and energy suppliers that are helping to save millions of pounds."

But Stockport head teacher, Jim Nicholson, said he was fed up with hearing this government line.

"We have seen how our colleagues are having to lay off staff and our vulnerable pupils are not getting support.

"We'd all rather be back in school teaching. But we've had enough," he added.

The head teachers taking part in the protest are from areas including:

Blackpool • Bolton • Brighton and Hove • Buckinghamshire • Cambridgeshire • Cheshire • Cornwall • Cumbria • Derbyshire • Devon • Dorset • Dudley, West Midlands • East Sussex • Essex • Gloucestershire • Greenwich • Hampshire • Hertfordshire • Kent • Kingston-upon-Thames • Lancashire • Liverpool • London • Norfolk • Northampton • Oxfordshire • Peterborough • Poole • Portsmouth • Richmond • Rotherham • Sheffield • Slough • Solihull, West Midlands • Somerset • Southend • Southampton • Staffordshire • Suffolk • Surrey • Thurrock • Walsall • Warrington • West Berkshire • West Sussex • Wigan • Wiltshire • Wokingham, Berkshire • Wolverhampton • Worcestershire