The 567 voters in the combined polling districts of Whalsay and South Unst returned a Leave vote of 81 per cent - the highest north of the border so far identified.
All of Scotland’s 32 council areas returned a pro-Remain vote, with a majority of Scots across the country backing the UK’s continued membership of the EU.
But research by the BBC has found pockets of firm pro-Leave support in Scotland, particularly in areas with connections to fishing.
Many residents on Whalsay are dependent on the industry, which has had regular disputes with the EU over catch quotas in recent decades.
The small community was also rocked in 2012 by the so-called Black Fish scandal when 17 skippers - most of them from Whalsay - and a processing firm were found to have netted £47.5m in the biggest fishing scam in Scottish history.
In the early 2000s Whalsay was often referred to as “millionaires island” as it was said to boast more millionaires per head of the population than any other place in Britain.
At least 20 skippers and former vessel owners on the island are reckoned to have amassed seven-figure fortunes from the sea.
The BBC analysis also found six wards in Banff and Buchan - another area with strong links to the fishing industry - returned a Leave majority of 61 per cent.
An Taobh Siar agus Nis, a ward at the northern end of the Isle of Lewis, also narrowly backed a Leave vote.
The closest result in a council area was in Moray. The Remain campaign won the north-east county by just 122 votes.
Fishing industry leaders in Scotland fear the sector could be used as a bargaining chip as ministers negotiate the UK’s exit from the European Union.
UK-registered boats landed 708,000 tonnes of seafood, worth £775 million into ports in the UK and abroad in 2015.
Scottish vessels accounted for 62 per cent of the quantity of landings by the UK fleet - more than double the English fleet.