Diplomatic immunity has to be *requested* by Ecuador, and the UK government can choose to grant it or not. In Julian's case, Ecuador did ask for diplomatic immunity and the UK said no.
The treaty that provides protection for Ecuador's genuine diplomats also says that they shouldn't smuggle him out. So for their own protection, the diplomats won't want to be involved in "sneaking him out".
Regarding "diplomatic vehicles", I don't think the building has a garage? I thought it was just a flat. In that case, he'd have to come out the building and through an area where he could be legally arrested, to get in the vehicle. Then he'd have the same problem trying to get out the vehicle into a plane. I'm not even sure if a diplomatic vehicle would provide any protection if the police knew there was a wanted fugitive in there.