How much is "much"?
If the trade's there, NZ will be there, guaranteed.
NZ sure did find other markets after UK entered the EU, and so has Oz, but our great friend China is a bitch to trade with, so a more diversified market is in NZ's favour.
Same with UK, has to renegotiate new agreements, take up to 10 years to fully get going, according to some.
The new agricultural policy that's going to come out of this Brexit vote will be an eye-opener.