Just over half (54 per cent) of respondents approved of the Government's decision to allow schools to select up to 15 per cent of pupils and would like ministers to go even further.
ATL spokesman Richard Margrave said that although it was interesting that most people appeared to favour selection, the figures should be treated with caution.
The strongest support for bringing back grammar schools came from voters aged 45 and over while 18 to 24-year-olds, many of whom had been through the comprehensive system, were less keen.
The biggest grammar school fans were in the lowest socio-economic groups. Just over half (55 per cent) of respondents in groups D and E wanted to bring back the 11-plus compared with 49 per cent from social groups AB.
Mr Margrave said: "The poll shows poorer people are having a tough time, sending their children to the local, under-resourced comprehensive. They are looking back with nostalgia to a period when grammar schools appeared to be doing the best for children."
The poll was carried out between January 12 and 14 on a sample of 980 men and women aged over 18.