OK, the poll was for the Daily Mail, but it was not of DM readers.
The margin is small at 51% Leave to 49% Stay, but the main thing is that immigration is cited as the main reason for leaving. The margin will be even bigger if the government does not get on top of immigration as almost half of those currently voting to stay in could change their minds if nothing is done.
The figures, if nothing is done, are remarkably similar to other recent polls asking whether the UK should take in more immigrants - about 75% No to 25% Yes.
Politicians can only march out of step with the people for so long.