In an unusual move, Mr Bercow has put his name to a letter intended to put pressure on Chancellor George Osborne ahead of the Spending Review.
Two Conservative former cabinet ministers and two ex-Labour cabinet ministers have also signed it.
The Department for Education said per-pupil funding was being protected.
It said the government would continue to make "funding fairer".
The letter to the prime minister, seen by BBC Radio 4's PM programme, demands "urgent action" to change the funding system.
It says the current school funding rules are arbitrary and unfair and see the worst-funded areas receive on average Â£2,000 less per pupil than the best-funded each year.
It comes as the Institute for Fiscal Studies says despite a Conservative promise to raise school spending with student numbers, the amount spent per pupil is likely to fall by around 8%, taking into account inflation experienced by schools, by 2020.
The IFS says this will be the first time since the mid-1990s that school spending has fallen in real terms.
Rising wage costs and national insurance bills are putting school finances under pressure.
The PM programme has heard fears those pressures could see classes of 50 pupils in core subjects.
Conservative ministers have long promised to change the formula that dictates how much money schools get, but have not said when the change will come.
If delivered without extra funding it would see some schools lose money.
The Conservative former chair of the education select committee Graham Stuart admitted the reform would be "enormously difficult politically".
The government needed to come up with a plan that was fair and politically deliverable, he said.
He added: "It's also about looking people in the eye and saying there is no rational basis for the additional funding that you receive compared to these other authorities.
"Therefore it is right and proper that your budget should be reduced."
Many Conservatives regard a manifesto commitment to "make schools funding fairer" as vaguely-worded and fear ministers will offer only slight change, late in the Parliament.
As speaker, Mr Bercow is politically impartial but can deal with his constituents' problems like other MPs.
Other signatories to the letter, which will be sent to the prime minister, include former Tory cabinet ministers Caroline Spelman and Cheryl Gillan.
Former Labour cabinet ministers Ben Bradshaw and Andrew Smith have also signed.
Their letter demands "urgent action".
It says: "It is widely acknowledged that the existing school funding model is a muddle and that funding for individual schools with similar pupil characteristics is arbitrary and unfair."
Nick Binder, head of the Sele school in Hertford and chair of the Hertfordshire Association of Secondary School Headteachers, told PM some heads were looking at teaching two classes simultaneously.
The plan could see one teacher addressing 50 children, he said.
"I don't think parents have seen the impact yet and I think as they do they are going to be shocked," he said.
A spokesman for the Department for Education said: "We are ensuring schools across England are funded fairly so all pupils, whatever their background and wherever they live in the country, have access to a good education.
"We have maintained per pupil funding and will make funding fairer.
"Despite the economic climate we have already committed an additional Â£390m to the least fairly-funded areas in the country.
"It is down to councils to determine exactly how funding is allocated to individual schools."
Speaker John Bercow has joined more than 90 Conservative MPs demanding the government urgently rewrites the rules for funding schools in England.