Members of the NASUWT, meeting in Bournemouth, criticised a loosening of the rules on who schools can employ to teach children.
The government says the changes allow schools to hire talented people and the vast majority of teachers will continue to have the recognised qualification.
But the union says it is about saving money.
One delegate told the conference children were being taught "on the cheap".
Last year the government relaxed the rules in England on employing teachers for academies.
The semi-independent state schools are now allowed to employ teachers who have not qualified as teachers, bringing them in to line with the situation in free schools and private schools.
In other state-funded schools, people employed as teachers have to have passed the relevant qualification - known as Qualified Teacher Status (QTS).
At the time, the government said the change would allow schools to bring in talented professionals such as scientists, musicians and university professors, plus experienced teachers and heads from overseas and the independent sector.
Schools are also allowed to employ people called "instructors" who have particular - usually vocational - skills but do not have QTS, and the rules governing when they can be hired were relaxed last September.
The NASUWT says the changes mean less-qualified people are being put in charge of classes - and are being paid less than teachers.
It has published a survey of its members which found six out of ten of those who replied said unqualified staff were being used in their schools and that most said unqualified staff were teaching lessons.
It asked for views from 2,300 of its members online earlier this month.
Chris Keates, general secretary of the union, said: "The extent of the secretary of state's decision to remove the entitlement of children and young people to be taught by a qualified teacher can now be seen.
"Parents and the public should be deeply concerned at the results of this survey. Now when a parent sends their child to school they have no idea who is teaching them.
"If any suggestion was made that unqualified doctors were let loose on patients there would be public outrage."
Head teachers' leader Russell Hobby described the changes as "limited" and said he did not think heads would be looking to employ unqualified staff.
The leader of the National Association of Head Teachers said: "The vast majority of head teachers will seek out good teachers with QTS, as long as that remains a strong qualification."
On the conference floor, union member Victor Aguera said: "This government has turned back the clock to the 1850s and is returning to a 'teacher monitor system'.
"Children are being taught on the cheap. It's part of the privatisation of education."
A spokeswoman for the Department for Education said: "It is simply not true to claim that this is about depressing costs. This is about raising standards.
"Independent schools and free schools can already hire brilliant people who do not have Qualified Teacher Status.
"We have extended this flexibility to all academies so more schools can hire great linguists, computer scientists, engineers and other specialists who have not worked in state schools before.
"We expect the vast majority of teachers will continue to have QTS. This additional flexibility will help schools improve faster, and give head teachers the freedom to hire the person best suited to their school."
The NASUWT passed a conference motion to work with others to "ensure that all those working in schools have appropriate qualifications".
The NUT, meeting in Liverpool, passed a similar motion.
More children in England are being taught by unqualified teachers, a teaching union is claiming.