Next Monday, here in New Zealand, we celebrate the official birthday of Queen Elizabeth II with a national holiday. This happens on the first Monday of June every year.
And, New Zealand remembers the sacrifice of their armed forces with a national holiday on ANZAC Day (25th April, or following Monday if it falls on a weekend). This is principally centred on the fighting alongside the UK in both world wars.
And, New Zealand recently voted to keep the current national flag, with the Union Jack in the top left quadrant. http://www.electionresults.govt.nz/2016_flag_referendum2/
There really is a very strong affinity for the UK here.