If Brexit happens and they leave the EU...

will GBP/USD lose correlation with EUR/USD?

Well, there is a huge chance for that. For years GBP/USD is positively correlated to USD/EUR and negatively to USD/CHF, but getting out of EU will be big for UK. And unfortunately, for any reasonable people, big meaning negative. UK is not nearly as strong of an economy as it was before, established on the Empire that has colonized 3/4th of the world. They still have tons of big companies established back in its strongest year, but even those native for British market companies will gladly focus on other markets, when they see that UK alone is simply not good enough. It also depends on their regulations with the EU later, in which prospering economies like Germany and even smaller ones, like Belgium and Netherlands are on a rise. Gotta admit, that Ireland really did a smart choice by separating themselves as much as they could and building a totally independent economy.

Brexit is happening and we are leaving. Neither will it be negative for us, except perhaps a bit of short term pain for long term gain. Only one nation will gain from Brexit, and that is the UK

IMO, chances are that there will be some loss of correlation. The amount depends on how split their economies and trade agreements are.
But in general. We might continue to see correlation between sterling and euro. Due to the proximity effect between economies. It is still easier/cheaper to import/export from countries close to yours. Thus wealth (poverty) in either country will have some spillover effect on the neighbouring countries.

Iris 11
You say Ireland is independent Economy ! LOL
Do your Homework-It is in the EU, It has the Euro as it,s currency.
It does what it is told by the EU
You only have to look at how the EU is "using Ireland as a Puppet" to thwart
the Uk,s long overdue Brexit plans.
75% + of Irelands economy depends on UK
As cat says- there will undoubtedly be a short term gain- but i think in 5 years
time we will look back ( with the other nations that will join us in leaving) and think how lucky
we were to leave the sinking EU ship - because as history tells us "BIG is BAD" and ALWAYS
ends in tears