Most important: They shouldn’t rush it.
I know, I know: A quick exit what all the continental Europeans are urging. As are the usual airheads at publications like The Atlantic. But that wouldn’t be in the UK’s interest. Or anyone else’s, really.
The formal mechanism to leave the EU, under the relevant treaties, is Article 50. Once an Article 50 notice is tendered an automatic two-year clock starts ticking and EU treaty benefits automatically fall away (for the tendering member state) at the end of that time.
After the June 23 referendum, but before she invokes Article 50, the UK holds all the cards with respect to timing and process. After she tenders, she’s at the mercy of France, Germany and the rest of the EU to get a deal agreed; the other nations can dig in their heels, run the clock out and threaten to leave her out in the cold (with no trade or visa deal) unless she agrees to their preferred terms, no matter how onerous. It’s a bit of mutually assured destruction, but it would weigh on the UK worse.
And while the people of the UK clearly want out of the EU, it’s also fairly clear that even the Brexiteers still want some deal with Europe covering trade, visas, financial services and such-like. They don’t want to wall themselves off like Tokugawa Japan.
So the UK should begin discussions promptly without formally tendering the Article 50 notice. At the least, they should get heads of terms publicly agreed and ratified with Brussels before invoking Article 50, spending the remaining two years papering the details. It also pays to see whether any other countries will join the UK in leaving — there have been rumblings. A coordinated exiting bloc could create their own trade club to cushion any blow, and have more leverage when negotiating collectively with the rump EU; but it only really works if they can remain more or less united and on the same timetable.
If the British deliver notice now they lose the whip hand and give all the negotiating leverage to the continentals, which is a terrible idea. Only someone as nefarious and obtuse as Angela Merkel would try to trick or bully them into giving up their leverage for nothing at the outset.
France and Germany have, after a few days, slowly come to realize this, so have opened with a refusal to negotiate ahead of an Article 50 notice. This is just the opening act of the kabuki, though, and while it’s unfortunate that the continentals decided to play it this way (such stance probably adopted pour encourager les autres), the UK government should keep trying to open negotiations, either publicly or behind closed doors. And if the continentals, against all reason (and everyone’s best interests, including their own) continue to refuse to negotiate before an Article 50 notice is tendered then the UK should promptly commence trade negotiations with as many of China, Japan, the U.S. and Canada, Australia and New Zealand, South Africa, the Southern Cone countries (Brazil / Argentina / Chile) as they possibly can, while still withholding notice. If the British can act like an independent power and arrive at suitable trade terms with enough other major world economies, they can more credibly stare down the continentals while the two year clock is ticking and refuse punitive or onerous terms.
And for those who say that the uncertainty is killing the markets, you know what would kill the markets worse? A bad deal which depresses the UK economy and hits hard on German, French and Italian exports. Or a full-blown internecine conflict in Western Europe; those also tend to be bad. The continentals seem emotional and hell-bent on retribution, though, so I wouldn’t trust their judgment or self-interest as the sole safeguard against a disastrous trade war. They just might do it out of spite, to everyone’s detriment. British assurances that they will continue to trade on existing treaty-guaranteed terms, and not end them until they can be certain of suitable replacement terms, will do far more to calm the markets and promote prosperity than an irrevocable blind leap into the unknown. To tender an Article 50 notice without knowing what to expect would be to place the UK’s future relationship with all of continental Europe entirely at the mercy of the inflamed passions of the French, and the plodding obstinacy of the Germans.
For all his faults, I have to imagine that this is the sort of thing that Donald Trump understands intuitively. The question is: Does Boris Johnson?