The UK does not cover its milk needs. Its self-sufficiency rate is 88% (year 2015).
During 2015 the UK imported 494,000 tons of Cheese, which corresponded to 1,803 million Euro, and 106,000 tons of Butter, which corresponded to 363 million Euro.
The UK largest supplier is Ireland, covering a share of 22% of the imported Cheese and a share of 62% of the imported Butter. Also the other major suppliers are EU Countries.
Membership in the EU is binding on the UK to place a duty on imports from New Zealand and Australia. This limit would fail with the UK exit from the EU, and in this case the historical relations between the UK and the two Oceanic countries (Commonwealth) could facilitate the trade between these countries.
In this scenario, if the differential between Oceania prices and the European prices will remain, the UK could find cheaper to import from New Zealand.
The EU Countries could then be affected by the UK exit, and particularly Ireland, which is on one hand the main supplier of Cheese and Butter, on the other hand finds in the UK its largest customer for these two products.
How will Brexit affect UK export? Imports to EU countries would be subject to duty, unless bilateral agreements will be reached.
After having analyzed the possible scenarios, and having overcome the emotional impact of Brexit, it is desirable that the parties find a compromise.