The New Zealand dollar was little changed near a 12-month high and may rally further if Britons vote to remain in the European Union.

The kiwi traded at US71.80c at 5pm yesterday, having earlier risen to US71.88c from US71.45c late on Wednesday.

The trade-weighted index was 75.99, having briefly touched a 13-month high of 76.06 from 75.87 late on Wednesday.

The latest two polls in Britain show the "leave" option, or Brexit, has slightly more support than remaining in the European Union.

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By contrast, bookmaker Ladbrokes puts the odds of a "remain" vote at 76 per cent.

Financial markets appear to have latched on to the bookmakers rather than polls, and the pound strengthened ahead of voting in the UK.

Mark Johnson, senior foreign exchange and derivatives dealer at OMF, said if the "remain" camp wins and the New Zealand dollar rallies, the gains could be amplified by traders who had bet on a Brexit and a weaker Kiwi being forced to buy back their positions.

If the Brexit campaign wins, "there's going to be a risk-off tone" in financial markets, he said.

An elevated kiwi may encourage the Reserve Bank to cut interest rates because of the damping effect on imported inflation well below its target band.