I want to apply for a british passport would I be able to live and work in new zealan

Not just with a British passport, no, that's got nothing to do with New Zealand. Why would you think it does?

You still have to go through the whole NZ immigration process and visa application.

NZ was a British colony and I thought there were favorable arrangements for work visas and immigration between Britain and NZ, so I wouldn't say Britain has nothing to do with NZ.

Check with the British authorities as to what, if any, privileges that will get you in NZ.

Thank u every 1 people say that new zealand is part of the commanwealth

New Zealand is in the Commonwealth, but that has no effect on their immigration policy.

You can read up on it here:
http://www.immigration.govt.nz

Lots of countries are/were part of the commonwealth. It doesn't really effect immigration either way these days.

I meant a British passport has nothing to do with New Zealand

The UK and New Zealand DO have a reciprocal 'working holiday Visa' for people aged between 18 and 31, which allows you to live and work in New Zealand for up to 23 months. The same system operates between Australia and the UK, which is why London (and Sydney and Christchurch) are swamped with youngsters from these nations working behind the bars.

If you're older than this, however, no deal.

You will get better response on Australia and the Pacific forum, but this is a travel forum, not immigration one.

Yep you can't just walk into NZ and live and work here just
Because you have a British passport. You will need to go through the immigration process and apply for work visa,student visa,or whatever you are looking for,