Markets had been spooked by the new Covid-19 strain and no sign of a trade deal signed between the UK and EU on Monday.
But by the end of Tuesday, investors steadied their nerves as stock markets rebounded despite no sign of a trade deal and borders remaining shut.
The FTSE 100 index closed up 36.84 points, or 0.6%, at 6,453.16. On Monday, the flagship index lost 112.86 points, or 1.7%. The FTSE 250, which is primarily made up of UK-focused businesses, had an even better day, closing up 258.61 points, or 1.3%, at 19,950.72.
In Paris the CAC 40 ended up 1.4%, while the DAX 30 in Frankfurt rose 1.3%.
Josh Mahony, market analyst at IG Group, said: "UK markets are in recovery mode today, with yesterday's sharp slump in domestically-focused assets being partially reversed over the course of the day. Volatility seems to be a foregone conclusion as we head towards the year-end, with the Covid-led economic isolation of the UK serving to provide a heavy dose of reality of the kind of disruption that could come if negotiators fail to agree a deal by year-end.
"However, Brexit failure is not a certainty, and market sentiment over the coming week is going to be heavily dictated by the ability to find compromise on the remaining issues."
But the pound failed to follow the moves on the markets, falling 0.76% against the dollar as markets closed at 1.336 and down 0.26% against the euro at 1.097.
In company news, shareholders in DFS Furniture enjoyed the news that online sales soared by more than three-quarters over the 24 weeks to December 13 to help overall sales rise 19% compared with last year – offsetting the falls from closures due to Covid-19 restrictions.
Shares closed up 22p, or 10.5%, at 232p.
A long-running battle for telecoms giant Vodafone took a step closer to completion as the company offered to buy out minority investors in Germany's biggest cable firm Kabel Deutschland for €2.12 billion (£1.9bn).
The mobile phone giant has been embroiled in a legal spat since it bought a controlling 76.8% stake in the company seven years ago, with investors angry at the price paid in the deal.
Shares in Vodafone closed down 018% at 121.78p.
Budget airline easyJet said it has agreed a deal with Airbus to defer the delivery of new aircraft due between 2022 to 2024 until 2027 and 2028, as it suffers from the Covid-19 crisis. Shares closed up 775p at 17.8p.
Welcome Break owner Applegreen said it will be taken private after a €718 million (£653m) takeover deal by a consortium involving its founders and private equity giant Blackstone. Shares closed up 5p at 510p.
Weir Group said the sale of its oil and gas division has been delayed until the first quarter of 2021 – having hoped to complete it by the end of the year. Weir agreed in October to sell the arm to Caterpillar for £314m. Shares closed up 12.5p at 517.5p.
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