Sterling was trading around $1.45 ahead of the referendum on June 23 in which the UK voted to leave the EU by a margin of 52 per cent to 48 per cent.
"With recriminations, two main parties in turmoil and nothing but questions and uncertainty as far as the eye can see. I see no reason to buy the dip," said Kip Juckes, foreign affairs analyst at Societe Generale.
The euro has also fallen 0.6 per cent against the dollar, amid concerns that Brexit could destabilise Europe and lead to other departures from the Union.
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The FTSE 100 opened slightly lower on Monday, down 0.7 per cent or 42 points, despite the speech by Osborne that was designed to reassure markets before they opened.
The actual fall on opening was slightly less severe than futures markets predicted. Futures suggested the index would fall by 2.8 per cent.
Analysts said that though uncertainty reigned, investors hadn't finished selling their assets yet.
“Things are so uncertain that investors still do not have a clear idea how much of their risk assets they need to sell,” said Hiroko Iwaki, senior foreign bond strategist at Mizuho Securities.
“But it is safe to assume investors are not yet done with all the selling they need to. I wouldn't be surprised to see another 10 percent fall in share prices,” she added.
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