How does Brexit effect lengths of stay in Europe?

Sorry, incorrect.
The maximum stay in the Schengen Area for non-EU/Schengen citizens is 90 days in any 180. The Schengen Area is roughly the same as the EU, but not exactly. The UK (and Ireland, Bulgaria, Romania, Croatia and Cyprus) are in the EU, but not in Schengen. Norway, Iceland, Switzerland and the "microstates" are not in the EU but are in Schengen.
So, the UK (please, not "England") does not and never has counted as part of your 90 day limit. Please note the "in 180" clause, leaving and re-entering the Schengen Area does not give you extra time.

And, the UK has not left the EU. It plans to do so, target date 2018. Until then, nothing changes.

Nope - dead wrong. European Union has nothing to do with the Schengen agreement. The length of stay in UK is 180 days but only 90/180 in the Schengen zone as well pointed out in the earlier response. Just to confirm what Chris posted in case you don't believe just one poster.

Pat,

The so-called "Brexit" doesn't affect lengths of stay in Europe at all.

As you noted, visitors to the Schengen area (most of the countries in continental Europe) are allowed to stay 90 days in any 180 day period. The 90 day allotment includes your arrival and departure days. Therefore you could stay in Spain for the 90 day allotment, go to the U.K. for 90 days and then return to Spain (at least that's how I interpret the rules).

Even though the U.K. is part of the E.U., it was never part of the Schengen Agreement and administered a separate system called the Common Travel Area, which also applies to Ireland. Tourists are allowed to stay six months in the CTA. Although the U.K. has voted to leave the E.U., nothing has changed yet and likely won't for some time.

Therefore you could stay in Spain for the 90 day allotment, go to the U.K. for 90 days and then return to Spain (at least that's how I interpret the rules).

Not quite. Arrival and departure days count. So the day you travel from Spain to the UK would be day 90, but also day 1 of your UK stay. You would have to stay 92 days out of Spain in order to come back on day 181.
There are also many other ways to mix it, going out of and returning to the Schengen Area multiple times, so long as you never exceed the 90 days in any 180 rule.

Chris F.,

"Not quite. Arrival and departure days count."

I mentioned the arrival and departure day caveats earlier in my reply.....

"The 90 day allotment includes your arrival and departure days."

In the latter part of my reply, I only stated the more general version since I'd already provided specific information on arrival and departure days.