Fishing - UK names for New Zealand fish

Located here in New Zealand I'm not sure what the UK names are for some of
the species we might share.

In particular I'm would like to know if we share the following species and
if you have the same names for them as follows:

John Dory
Snapper (Not sure if found in UK waters)
Moonfish (Not sure if found in UK waters)
Groper also known as Hapuka (may be Sea Bass I think)

I have a website offering copper fish art and I'm trying to break into the
UK market but do I have the right names? If it's any help you can see the
fish at:
http://www.gift4myman.com/site/876260/page/45030.

Thanks in advance.

Jeff