As you will see here. He is, I think, the most prominent metropolitan, moderate/centre/centre-left Establishment person to come out of the Brexit closet.
The Economist, which perhaps occupies an equivalent place to Jenkins but on the right of the centre, does not favour Brexit, as you will see here.
The difference between the Economist and Jenkins appears to be largely based on their assessment of how attractive the outcome of a post-Leave vote negotiation would be. But that is all a matter of crystal ball gazing. I'd be more interested in what the superforecasters have to say about that than in their opinions.
More significantly, it is surely a sign of the utter lack of any appeal in Britain of the European dream - qua dream, ideal or aspiration - that there is a possible outcome to these negotiations that would persuade elite, educated, optimistic, progressive, metropolitan opinion of the Jenkins/Economist kind that Brexit would be a Good Thing. Britain's relationship with the EU has become purely transactional. That is just one would expect from a nation of shopkeepers, as an earlier unsuccessful proponent of European integration described us, and not at all a bad thing for our political masters, both here and abroad, to bear in mind.