I presume you're referring to Brexit, but this seems to be mostly a strong US dollar and energy crisis story. Europe is in a similar situation so I'm not sure what difference staying/leaving would have made.
In this specific case it's not really a "strong dollar/energy crisis" story – the proximate cause is a massive overnight shift in UK government fiscal policy to "let's cut taxes and not spending, and it will all work out" that's obviously spooked everyone.
Despite relying on them being willing to sell us energy, as non-single-market countries have no guarantee of access?
But I agree with the above sentiment anyway, same could be said for the Soviet Union and in many ways, Russia today.
The USD is strong, but that's only half the story here. Just look at EUR vs GBP since Brexit: down 20%. We're doing 20% worse than Europe, an economy with the same issues around energy as ours, plus no real decisive government and which just finished dealing with a debt crisis and a migrant crisis.
We weren't on the Euro when we were in the EU.
If you're just saying that it is not possible to know for sure whether Brexit is the cause of the 20% decline, well, you're right. Seems like a reasonable hypothesis though.
[1] https://www.google.com/search?q=gbp+to+euro (and set it to 5 years)
While your core conclusion may not change, you shouldn't do that; strength of currency is not a straight number you can use to measure the strength of an economy like that. GDP change would be better and I still think that one stinks too. Despite the use of the word "strong" it is definitely not the case that economies want their currencies to just be as "strong" as possible as you might think from the connotations of the word "strong".