Writing for the European Council on Foreign Relations, YouGov’s Peter Kellner highlights an important polling finding:
In July this year, YouGov asked this question: ‘Imagine the British government under David Cameron renegotiated our relationship with Europe and said that Britain’s interests were now protected, and David Cameron recommended that Britain remain a member of the European Union on the new terms. How would you then vote in a referendum on the issue?’…
Tory voters swing right round, from 58-29% for leaving the EU when we ask the conventional in-out referendum question [without Cameron's endorsement for a 'yes' vote], to 55-34% for staying in, if that is what the Prime Minister recommends.
The degree to which Conservative voters can sway a referendum result if they get a strong steer from their party’s leadership mirrors the experience of the AV referendum campaign. When Cameron started campaigning strongly for a no vote in that referendum, Conservative supporters switched in large numbers and the overall figures moved sharply as a result.