I'm no diplomatic expert and like opebo, I'm a lazy, so I'll ask - Isn't a diplomatic vehicle and a diplomatic plane the property of the foreign gummit? I'm guessing no or he'd be in Quito by now.....but enlighten me.
Yeah, they probably wouldn't enter Ecuador's car or plane (though I'm guessing Ecuador only used ordinary commercial flights), I think the issue is that even if he were transported without notice to the airport, he would still have to pass through some form of immigration control. Diplomats do as well - they have their own line for rushed service, but they still have to go though it. I imagine there are cases - maybe american diplomats, highly ranked members of governments, and I would even guess some of the super-rich, whose immigrations processing is taken care of on their own private plane, but a delegation from immigration, dealing with minions.
But the fact remains, everyone (other than maybe a head-of-state) who goes into and out of a country still has to have a passport, show it, and get stamped in or out. I don't think he could get out, leaving aside the idea of Ecuador deliberately violating British immigration law by smuggling him out in a bag, which I don't think they would do. Quite frankly I think it is far more likely that Britain will break with diplomatic protocol by simply removing him from the Embassy than that Ecuador will try to get him on a plane.