The NASUWT survey claims some parents are asked for £400 or more per year.
Schools in England have been warning of cash shortages and the union says schools are now depending on parents.
But the Department for Education says "no parent is required to make a contribution".
Teachers' unions are holding their conferences over the Easter bank holiday weekend, with funding one of the biggest issues.
The National Union of Teachers, meeting in Cardiff, will hear warnings on Saturday about the impact of cash shortages.
The survey from the NASUWT survey, holding its annual conference in Manchester, claims that schools are increasingly relying on money from parents.
Based on almost 4,000 responses, the survey says 18% of parents have been asked to sign up for direct debits or standing orders for their children's school, typically of about £50 per year.
But more than one in 20 parents with children in state schools were paying £400 or above.
A further 13% of parents had been asked to make donations in cash or cheques.
Your comments on schools asking parents to top up their budgets:
"She's only been there a term, but there seems to be a letter home at least once a week asking for money," a parent told the NASUWT survey.
"The school asks for a 'voluntary contribution' but if you forget to pay you are sent texts telling you that you haven't paid," said another parent.
There were other financial costs for parents, such as a laptop for homework and music lessons.
"We have not allowed them to do music at school as they need to provide their own instruments," said a parent, quoted in the survey.
Over a quarter of parents said their child had been unable to take part in a trip or excursion because of the cost.
"Ski trip was £600. French trip £450. These are for less than a week. They are beyond my funds," a parent told the survey.
The union's leader Chris Keates said that "access to education must not be based on parents' ability to pay".
This week the Sutton Trust education charity warned of schools cutting staff because of financial pressure.
The Public Accounts Committee has said that standards are threatened by school budget cuts of £3bn.
A lobby of Parliament over funding, by teachers' unions and parents' campaign groups, has been announced for early June.
Kevin Courtney, NUT general secretary, reminded the government of a manifesto commitment to parents that "the money that follows their children into schools will be protected".
"In half of the schools in the country the money following your child into schools has been dramatically cut in cash terms, and in the other half it's been cut in real terms," he said.
A Department for Education spokeswoman said: "No parent is required to make a contribution to their child's education, the rules are clear on this and no policies have been introduced by this government to allow schools to charge parents."
The spokeswoman said school funding was at record levels, but "we recognise schools are facing cost pressures."
Almost one in five parents in the UK is being asked to set up payments to their children's schools, as head teachers warn of budget shortages, says a survey from a teachers' union.