When Britain was originally negotiating and then confirming by referendum its membership of what was then the European Community, one of the issues was New Zealand agricultural products. I need to go back and read the contemporary literature, but essentially the point was that Kiwi exports of butter and lamb were important to its economy and the UK wanted to continue to have access to them tariff free, so it was agreed that quantities of these products could enter the common market free of tariffs.
New Zealand subsequently adopted a 'scorched earth' farm policy which caused more pain than many of its admirers admit and was also accompanied by a devaluation of the NZ dollar (as well as freeing up the country's ports from various restrictions). New Zealand has thus opened up new markets for its dairy products in East Asia and the Gulf states.
Nevertheless, that does not mean that the European market does not matter. New Zealand has formally objected to a plan that would limit the amount of its lamb sold in Britain. The UK Government wants to share the tariff rate quotas with the EU after Brexit. The hope is that replicating the EU's tariffs and quotas would make matters easier in the World Trade Organisation.
It is somewhat ironic given that it was hoped that one of the first post-Brexit free trade pacts would be with New Zealand. You might wonder what the UK could export all the way to New Zealand, but apparently it is about financial services.