That's prompting concern not only about the impact on the UK economy, but a possible fracture of the wider European Union.
Investors are also reluctant to take positions ahead of the Federal Reserve interest rate decision on Thursday New Zealand time, boosting the appeal of safe haven assets such as gold, the Japanese yen and the Swiss franc.
"The market is bracing itself for several key events," said Martin Rudings, senior dealer, foreign exchange at OMF.
"We have an increase in volatility through the market and a lack of liquidity and essentially people are taking risk off the table. Money is pouring into safe haven assets. It's a very difficult week to navigate and I think a lot of people are sitting on their hands. It's very confusing and not for the faint hearted."
OMF's Rudings said the kiwi and Aussie were being held up by their relatively higher yields.
He said some certainty would return for the path of the US dollar after the Federal Reserve decision.
The kiwi could potentially jump to 52 British pence should the UK vote to leave the EU, and would likely fall to about 49 pence if the UK remains, he said.
Once decisions on these two events were known, investors would turn their focus to the US elections, he said.
In New Zealand today, data is published on May food prices.
The New Zealand dollar was little changed at 95.31 Australian cents from 95.33 cents following the Queen's Birthday public holiday in Australia yesterday. Australia has business confidence data scheduled for release today.
The local currency fell to 62.34 euro cents from 62.53 cents yesterday. It gained to 4.6366 yuan from 4.6318 yuan, and was little changed at 74.49 yen from 74.50 yen. The trade-weighted index edged up to 75.26 from 75.19.
