The FTSE-100 Index raced more than 1%, or 64.9 points, higher to 5870.5, while Wall Street's Dow Jones Industrial Average added around 120 points in early trade, buoyed also by more strong third-quarter US company earnings.
There were sharp gains across Europe amid the eurozone optimism, with the Cac 40 in France up 2.4% and Germany's Dax 1.6% higher.
Spain is understood to be ready to apply for a credit line which would pave the way for the European Central Bank to start buying bonds, easing concerns over the struggling country and the wider eurozone crisis.
Banking stocks were boosted by the improved mood, with better-than-expected third quarter figures from US group Goldman Sachs adding to the gains.
Goldman said it swung to a profit after revenues more than doubled, which overshadowed the shock news that Citigroup chief executive Vikram Pandit was resigning with immediate effect.
In London, Royal Bank of Scotland rose 11.9p to 280p and Barclays added 9.25p to 246.1p.
Lloyds Banking Group rose 6% to near the top of the FTSE-100 Index amid reports the Financial Services Authority has given the green light to plans to bolster its finances by swapping assets with its Scottish Widows life insurance arm.
Lloyds, which rose 2.4p to 42.8p, would borrow around £1 billion of liquid assets held by Scottish Widows under the deal by using a larger pool of lower quality securities as collateral in a bid to boost its cash position.
Mining stocks were also encouraged by the momentum in the eurozone, which comes ahead of a summit in Brussels tomorrow, as Evraz rose 14.5p to 243.7p and Polymetal International added 34p to 1160p.
Deteriorating trends in Europe's car industry dented engineering firm GKN after it reported some softening in order books.
Redditch-based GKN saw its shares fall 3% or 7.1p to 204.8p as it warned challenging conditions in Europe had offset stronger demand in the US and China and in its civil aerospace division.
Outside the top flight, Sportingbet pared earlier gains to stand 0.5p higher at 53.5p after the online gamer said it would back an increased 61.1p-a-share takeover offer from Britain's biggest bookmaker William Hill.