Most of Britain’s millionaires reckon Brexit will make them even richer, according to a survey by wealth managers at Swiss bank UBS.

A poll of more than 400 Britons with at least £1m in liquid assets in addition to their homes found that 78% thought Britain’s decision to leave the EU would have a “positive effect” on their financial plans.

Nick Tucker, UK head of UBS Wealth Management, said many of the bank’s clients were anxious about the effects of Brexit on their finances but most of the richest of the rich were “now taking a more positive view”.

“UBS Wealth Management doesn’t take a political view on Brexit,” Tucker said. “But our client conversations around the country have revealed significant levels of anxiety. This latest data of UK millionaires suggests a more complex picture. Over the longer term, most are now taking a positive view.”

The survey, published a week before Theresa May pulled the trigger on article 50 – the two-year process of Britain exiting the EU – found that young millionaires are even more bullish on Britain’s future outside of the bloc.

UBS found that 83% of millionaires aged 18 to34 thought Brexit would have a positive impact on their long-term financial planning. This compared with 70% of 35- to 44-year-olds feeling positive about the impact of Brexit on their finances, and 74% of over-64-year-olds.

According to polling data from YouGov, 75% of 18- to 24-year-olds voted to remain in the EU.

Three-quarters of the millionaires surveyed by UBS said they thought Brexit would have a positive impact on the overall UK economy in the long term, despite the collapse in the value of the pound since the referendum and concerns that it may be more difficult for the UK to trade goods and service after it leaves the EU.

However, Tucker said that despite being bullish about their personal finances in a post-EU world, rich people are holding an increasing amount of their wealth in cash to give them more flexibility in case of any financial shocks.

“We still see many investors holding on to cash, rather than investing,” he said. “This is especially true of younger investors. In an environment of returning inflation and low interest rates, we recommend looking for investments with a higher return – whether in the UK or around the world.

“UK assets have proven more resilient than feared and we expect this trend to continue in the coming months. Even with this positive picture, and the bullish confidence we see on Brexit, investors should still look for a balanced portfolio, rather than sticking all their eggs in this one British basket.”

The number of UK-based ultra high-net-worth individuals – those with more than $30m (£24.2m) in assets – is expected to increase by 30% to 12,310 over the next decade. Liam Bailey, Knight Frank’s head of research, said London would remain “the city of choice” for the super-rich from Asia and the Middle East despite concerns over Brexit.

“In a European context, London is without doubt the dominant city for the wealthy,” he said. “London is just more accessible for more wealthy people, it is more convenient, more connected and more open than other cities. London attracts talent from around the world, and it will continue to do so.”

Bailey said Brexit may have some impact on London’s global appeal, but the UK’s membership of the EU was less important for the world’s richest people than the general population.