In an ominous warning to the Prime Minister, about 60 per cent of those surveyed by the ConservativeHome website said the deal as outlined so far would be bad for Britain if implemented, and the same proportion said they would not support it.
By contrast, 31.5 per cent of the website’s 1,225 opinion panel members thought it would be good for Britain, while 33 per cent said they would back it.
About 6 to 8 per cent did not have an opinion.
The website said the speed of the response to the poll was striking as it was issued on Saturday when England was facing its crucial World Cup quarter-final and Downing Street’s promotion of the plan was dominating headlines.
Separately, pollsters Survation said 33 per cent of the 1,000 people interviewed for its online poll on Saturday backed the deal against 23 per cent opposing it.
Survation also found support for Labour had gone up two points since June 21 at 40 per cent, while the Tories were down three, on 38 per cent.
More than a third also said Mrs May should lead the Tories into the next election with 24 per cent wanting her to quit.