I saw the interview with the Turkish official on Newsnight. They are very disillusioned now that their only real supporter turns out to have been humouring them along. It's not like Cameron will be PM for much longer anyway.
We do want Turkey to Westernise, and we need favours from them from time to time, so it makes sense from our own interests to encourage them, but they are going backwards in their EU ambitions under Erdogan at the moment on so many issues like human rights, treatment of minorities, press freedom, corruption and so on. In 10 years they've managed to achieve the science and research chapter - 1 out of the 35 conditions for membership and in most areas they've not even made a start.
Any EU country can veto them joining if they ever get close, with Greece and Cyprus some obvious candidates to do so, and France and Austria would have a referendum on it. I'm not sure anyone is really keen in Europe for them to join. Even within Turkey support for joining has declined.
If by some miracle they do join it will be decades away and 7 years transitional immigration controls on top of that. We may well have had another referendum by then. Turkey would also be a very different country if they achieve membership.
fullfact.org/europe/turkey-likely-join-eu/