Britain's FTSE 100 Index climbed more than 2%, up 132.1 points to 5737.7, having sunk to a two-month low last week on fears that political deadlock will prevent a resolution to the US fiscal cliff.
But reports of positive talks between Republicans and Democrats in Washington have boosted confidence, with the Dow Jones Industrial Average up 1% at the time of London's close.
Markets in Germany and France also rallied on hopes that another meeting of EU finance ministers on Greece's bailout programme later this week will be positive.
There was a boost for the euro as a result, with the pound down against the single currency at 1.24 but slightly higher against the US dollar at 1.59.
Barclays topped the FTSE 100 risers board after investment bank Goldman Sachs introduced a buy rating on the stock and said it was optimistic about the troubled bank's ability to achieve substantial value for shareholders.
The blue-chip stock was 15.55p higher at 249.75p, while elsewhere in the banking sector HSBC lifted 22.5p to 618.3p after confirming talks over a deal to sell its stake in China's Ping An Insurance. Analysts think the sale could generate up to 3 billion US dollars (£1.9 billion) for the banking giant.
BP shares improved 15p to 431.6p after a newspaper report suggested it was contemplating whether to commit £3.7 billion to a massive share buy-back that bosses hope will revive its flagging share price and thwart possible bid suitors.
A 2% surge in the price of Brent crude to 111 US dollars a barrel amid escalation in the conflict in Gaza was also responsible for some of BP's rise.
Elsewhere in the commodity sector, improved economic optimism in the US meant Eurasian Natural Resources lifted 5% or 12.5p to 272.1p and Randgold Resources cheered 305p to 6655p.
Online supermarket group Ocado topped the FTSE 250 Index with a jump of 24% after lenders including Barclays and HSBC agreed to extend the company's £100 million loan facility until July 2015.
With existing shareholders also backing a £35.8 million share placing in the wake of improved trading figures, shares surged 14.45p to 75p.
The new shares were priced at 64p a share, representing a 6% premium on Friday night's price, but this was still 65% lower than the company's flotation price of 180p a share in July 2010.
Elsewhere, shares in Bristol-based outsourcer MITIE fell 3%, off 10p to 280p, after it said pre-tax profits fell 13% to £37.7 million due to £4.8 million of restructuring and redundancy costs. Underlying profits were up 2% to £48.8 million, helped by the start of its largest ever contract with Lloyds.
Aga Rangemaster's shares jumped 11% or 6p to 62p after it said trading for its major brands had shown encouraging signs, driven by the launch of new ranges.
Meanwhile, Majestic Wine shares were 11p higher at 476p after it reported a 4% rise in half-year profits.
The biggest FTSE 100 risers were Barclays up 15.55p to 249.75p, ARM Holdings ahead 36p to 747p, Eurasian Natural Resources 12.5p higher at 272.1p and Randgold Resources up 305p to 6655p.
The biggest FTSE 100 fallers were Melrose down 2p to 206.9p, G4S off 1.7p to 242.4p, Pennon 1.5p lower at 598p and Shire down 2p to 1727p.
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