I won't post the video again, but leading Leave campaigners (Farage, Johnson, Hannan) were saying 'nobody is talking about leaving the single market' and pointing to Norway and Switzerland as the way forward. If it had been explicit on the ballot paper that the vote meant leaving the single market, the customs union and all other EU institutions, Leave would have lost heavily.
Cameron and Osborne who led Remain both emphasised consistently that Leave meant out of the single market membership. Gove for Leave agreed we would lose membership. References I have found to Johnson leading up to the referendum have him stating that we would still have access to the single market. I have not found him claiming we would retain membership.
