The study by BMG Research for 'The Independent' newspaper also showed that most people think the number of individuals holding fascist views is increasing in the UK and on the continent as well.
A majority of British people now believe the dark shadow of fascism is spreading across the United States following Trump's shock victory in November 2016, it said.
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53 per cent said they believed it is growing, just three per cent said they thought the number of people is decreasing, while 20 per cent said it is about the same.
When the same question was put in relation to the UK, almost half, some 46 per cent, said they believe the number of people with fascist views in Britain is growing, with three per cent saying it is decreasing and around a third believing it is about the same.
Looking at Europe, the figures were broadly similar, with 48 per cent saying they believe the number of people with fascist views is growing.
BMG Research Director Dr Michael Turner said: "With age comes experience, which may explain why our polling shows that it's older Britons who are most likely to feel that fascist views are on the rise, particularly in Europe."
He added: "Remainers are much more likely than Leavers to feel that fascist views are increasing at home.
Around six in 10, 59 per cent, of those who voted to stay in the EU feel that fascism is on the rise in the UK, whereas just four in 10 Leavers, 41 per cent, feel the same.
"However, both Remainers and Leavers are much more united on the view that fascism is rising on the continent, with some 57 per cent of Remainers and 52 per cent of Leavers saying so in our latest poll for 'The Independent'.
Official UK Home Office statistics have revealed an equally worrying hate-crime spike in the UK since the vote to quit the European Union.
In July, there was a 41 per cent increase in the number of racially or religiously aggravated crimes recorded by police.
They correlated with earlier figures which showed the number of alleged racially or religiously aggravated offences rose by 58 per cent in the week following the June Brexit vote.
In 2017 elections in France, Germany and Holland are expected to see far-right parties make stronger bids for power than at any moment in recent history.
BMG Research interviewed a representative sample of 1,507 UK adults online between December 1 and 5.
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