It also predicts an increase in the number of children being bussed to schools as their nearby local primary cuts classes - prompting particular problems in rural areas.
The survey looks at what 12 of the first 60 authorities to receive Government grant to cut class sizes are doing and how 22 of the remaining 86 are planning to respond over the next two years.
It shows that many authorities in the first tranche have begun building work to accommodate the additional classes needed. Extra teachers have also been employed.
Some councils are considering a single admissions date. The NUT said this could lead to young children being admitted to inappropriately staffed and resourced classes.
Doug McAvoy, general secretary, said problems were inevitable but added:
"That should not detract from the benefits the reform will bring to education of children now in smaller classes The survey's findings chime in with warnings sounded by the consultants Coopers and Lybrand earlier this year. In April it claimed six out of 35 local authorities intended to create mixed-aged classes to fulfil Labour's manifesto commitment and a further 12 might follow.
Six councils were going to provide extra accommodation while 23 were considering it.