Now Matthew Holehouse has pointed to another pair of polls, one each on behalf of different sides of the question, and getting rather different answers due to their rather different question wording.
One gets 57% in favour of staying in the ECHR, with a question naming it and mentioning a positive of it, while another gets 54% supporting leaving it, with a question emphasising illegal migrants:
UPDATE: And here is a third example, this time from Deltapoll.
From what you know, do you think the United Kingdom should withdraw from the European
Convention on Human Rights, or stay in it?
The UK should withdraw: 26%
The UK should stay in it: 49%