But, they needn't have worried, really. The stock markets have taken the referendum in their stride, surging for the fifth consecutive day to put on another 1.2 per cent and close at 6,338.10 at the end of official trading.
Sterling also had another bumper day, reaching its highest level of 2016, up 0.8 per cent at $1.4824 by the time the London markets closed for the day.
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As traders believed the Remain rally could have already run its course, it was riskier sectors - most vulnerable to Brexit swings - that outperformed the index. Barclays rose 2.7 per cent to end at 187p. That was the bank's highest finish to a session since January and completes a 17 per cent climb in just one week.
The Royal Bank of Scotland (RBS) ended up 1.6 per cent at 250p a share - also 17 per cent higher than this time last week.
Jasper Lawler of CMC Markets said: "Lighter volumes are causing some erratic price moves with many traders sitting on their hands under after the referendum result.
"Investors who wanted to protect their portfolio against adverse moves in sterling or other UK assets will have done so already. With polls now showing a bias towards a Remain vote, there is no need for any more hedging."
As Remain stretched ahead in the final opinion polls published yesterday - and the odds of a vote to Leave hit a record 7/1 at one point - European markets also jumped. The Dax in Germany stood up 1.8 per cent and France's Cac 40 climbed 1.9 per cent.