"Complex arrangements"? Things like landing fees, airport taxes, etc.? I didn't think they were affected by the EU anyway.
The EU affects the way airlines operate quite heavily. International Aviation is a bizarrely run and quite protectionist affair - generally, an airline is only allowed to operate flights too and from it's country of origin with a few key exceptions (ie, a stopover on route to a final destination).
This is why British Airways for example is legally prevented from operating a flight from, say, Cape Town to Toronto.
The EU changes this by allowing all of it's member states to be counted as one 'area' for the purposes of these rules. So, Easyjet can fly London to anywhere, but also EU to anywhere, or anywhere to where within the EU.
Presumably the argument about higher air travel costs relate to the fact that quite a lot of the routes currently operated - which contribute to overall margin - would be illegal and would have to stop, or would need to involve setting up entirely new subsidiary companies within the EU.
For example Norwegian's flights from Gatwick to North America can only operate as a result of the EU.
I'm sure the rebuttal will be 'well we'll just agree something!!111' but nobody else in the world has done that...