Thanks for the link. I've read through the quotes, and I can't find any instance of Johnson making a promise during the referendum campaign to keep the UK in the single market. I don't understand how he could have made such a promise even if he had wanted to, since he would have had no power to keep the commitment at the time — he didn't become Prime Minister until years after the referendum campaign. In 2016 he wasn't part of the government and wasn't seeking to be, at least not openly. He had no authority to make promises about future policy, and he wasn't proposing to replace the Cameron government.

What I see in the quotes in the link is Johnson expressing a personal preference for the UK to retain access to the single market and influence in its governing structures, in remarks made in 2013, a few years before the referendum was held. He talks about his voting intentions — at that time, he was the Mayor of London and had no vote in Parliament, so he is referring to how he might vote in what was, at that time, a hypothetical future referendum. The wider context, which is apparent from the contemporary reporting [1], is that, at the time, he was calling for the Single Market to be reformed, and for the UK to leave most of the EU's structures, but to remain part of the reformed market. A couple of years later, Cameron attempted to secure some reforms to the UK's relationship with the EU, but he focused on immigration and welfare rather than the Single Market. Cameron then presented the reforms (such as they were) as part of the basis for his support of the UK's continued membership of the EU during the referendum campaign, but no changes to the Single Market of the kind that Johnson had called for earlier were agreed.

My recollection of the role of the Single Market in the referendum is that the official Leave campaign was pressed to take a position on retaining Single Market membership; that they ultimately came down in favour of leaving (in order to remove the UK from the jurisdiction of the ECJ and allow EU regulations to be repealed); and that Johnson (who was part of the official campaign) subsequently adopted that official campaign position in his public statements. During the referendum itself he therefore supported leaving the Single Market, at least in its unreformed 2016 incarnation.

My memory is that the key statement of the official Leave campaign's position on the Single Market was made by Michael Gove on the Andrew Marr show. I remember it because the Leave side had been under pressure to make its position clear at the time, and Gove's response on the show seemed to signify that they had chosen to bite the bullet and accept leaving the Single Market. On the one hand, adopting a clear position meant that they couldn't be accused of equivocating on the subject any longer, but on the other hand, the Remain campaign was then able to argue more strongly that the Leave side was embracing trade disruption. Here's the relevant quote from the transcript of the Marr show[2]:

'Marr: Let me ask you, just before we leave the economics actually, a very simple question I have tried to get an answer to from various people on your side – is should we or should we not be inside the single market? Do you want us to stay inside the single market? Yes or no.

Gove: No. We should be outside the single market. We should have access to the single market, but we should not be governed by the rules that the European Court of Justice imposes on us, which cost business and restrict freedom.'

The BBC reported at the time that Gove's answer on the Marr show was a response to the pressure to clarify the Leave campaign's position on the Single Market.[3]

Incidentally, with regard to Johnson claiming to be a fan of the EU; I don't personally find this surprising. He has a well-publicised affinity for European civilization; in a book about ancient Rome that he published some years ago, he wrote approvingly about the ability of the Empire to unite diverse peoples as citizens of a common European state, and contrasted that history with the EU — the book was adapted into a television series for the BBC that he presented. His father also used to work for the European Commission; before he was sent off to Eton, he, his siblings and his future wife were educated at a school in Brussels that was established for the children of EU staff [4]. It may be worth noting that the comment was also somewhat qualified; he said that 'in some ways' he was 'a bit of a fan'.

[1] https://www.independent.co.uk/news/uk/politics/boil-it-down-...

[2] http://news.bbc.co.uk/2/shared/bsp/hi/pdfs/08051604.pdf

[3] https://www.bbc.co.uk/news/uk-politics-36084457

[4] https://en.wikipedia.org/wiki/European_School,_Brussels_I