The Brexit will lead to an eventual return of the UK's historic divide-and-rule "balancing" policies vis-a-vis Continental Europe.
They're still practicing these to a mild extent, but it's nothing like it used to be.
What can be foreseen to happen as one of the most unexpected long-term results is London becoming more geopolitically active at interfering with EU processes, especially if a "nationalist" leader more amenable to this strategy comes to power and the "deep state" (permanent military-intelligence-diplomatic bureaucracies) aligns towards this policy.
This is the most "reasonable" foreign policy for dealing with Continental Europe and leveraging the UK's position as it faces internal disintegration pressure, too, though of course, governments don't always do the most "reasonable" things.
It's too early to forecast the specificities of what this would look like in practice, though it could likely take a layered approach of supporting EuroCautionary (a more positive-sounding euphemism for "Eurosceptic) parties and leading figures like Orban.
The combined effect would be to hit the EU at its most vulnerable point during its weakest moment.