If London was as smugly left wing as he the author thinks it is then it would not have voted Boris Johnson as mayor for two terms. The same Boris Johnson that was the head of the Leave campaign.
London is libertarian, or old school liberal, not left-wing, and Boris Johnson did just fine as an old school liberal mayor before he started agitating for Brexit.
It's a branch of libertarianism that believes that if laws and regulations must exist, they should be implemented at the highest possible level in order to ensure consistency and insulation from provincial arbitrariness.
The sort of 'libertarianism' that would advocate a world wide state than? To me that looks more like the ultimate in repression than in anything you might call liberty.
Exactly that sort of libertarianism. According to such a view, a world wide state would be less oppressive than a nation state because the center wouldn't have the sort of local knowledge to make repression truly effective, it wouldn't have the petty and internecine struggles that make local politics nasty, and it would have to fight through all the intermediate layers of administration in order to implement repressive policies. Because of this reason, small political units such as North Korea and Eritrea can be more oppressive than large ones such as Russia or China could ever hope to be, and most oppression in the United States takes place at the local rather than national level (e.g. excessive incarceration, civil forfeiture).
TL;DR: neighborhood bullies are far worse than the average dictator.
So from their perspective, the amount of repression one gets in a Soviet Russia or China is acceptable, and scaling it up to be worldwide could be considered libertarian? Or do they believe there is some way of stopping the worst people rising to the top in a worldwide government that doesn't exist at the Russia/China scale?
Too many people conflate what "globalism" (of the E.U. variety) has become with the libertarian program of open borders and free trade. The E.U. is a long march towards political unification. That's why you have libertarians who (rightly) oppose it.