"There's a range of different products that we pride ourselves on producing that would really benefit from an agreement that sees a reduction in those tariffs."
Laura Clarke, the UK's High Commissioner to New Zealand, said both countries saw free trade as a global good. The agreement may reduce tariffs on New Zealand agricultural products, but the UK would hope to reduce tariffs on areas such at gin and car parts.
"A UK New Zealand free trade agreement will send a strong signal in times of global disruption of two friends standing together against protectionism, working together to grow our economies."
New Zealand is already negotiating a free trade agreement with the European Union, although earlier this month Parker described leaked details of an offer from the trading bloc as a "very negative signal".
No timetable has been set for when the talks are hoped to be concluded.
According to MFAT, modelling undertaken by the UK Government estimated that a free trade deal could raise New Zealand's gross domestic product by close to $1b (after it was in place for 15 years), suggesting New Zealand's exports to the UK could grow by 40 per cent, while UK exports could increase by 7.3 per cent.
National's trade spokesman Todd McClay, welcomed the news, but said the deal struck needed to be similar to that reached with Australia.
"For a deal to be judged a success, it must be equal to our Closer Economic Relations (CER) Trade Agreement with Australia, and include unrestricted trade in agriculture products especially unencumbered access from New Zealand lamb and butter to the UK market," McClay said.
Catherine Beard, executive director of ExportNZ said as well as being New Zealand's sixth largest trading partner overall, it was the fourth biggest agri-food export destination and fifth-biggest source of investment.
"The UK also offers a high-value market for sophisticated niche manufactured products such as agri-tech and medical devices," Beard said.