Gibraltar is in a funny position in the EU, as it is not part of the customs union and it is not part of the Schengen Agreement, but is covered by rules on free movements of people.
That is why border although border posts are legal under European rules they have to be proportionate, as the EU reminded Spain today, and the Spanish probably wouldn't get away with some kind of tax for crossing the border.
The other threats: closure of airspace and damaging or restricting Gibraltar's internet companies, they may well be possible under European rules because there is no doubt Spain can damage Gibralta's economy.
The great irony is that they would also be damaging themselves - Gibraltar is one of the biggest employers in Southern Spain in the area around Gibraltar it is estimated that 15% of its GBP comes from goods and services provided from territory.
That is why the unions are furious about this move, and the local Spanish mayor wants nothing to do with this.
I suspect the reaction from Spain what will restrain this row, rather than European rules or pressure from London.