The FTSE closed 35.9 points higher at 6282.8 in a marked recovery after Monday's 100-point slump on concerns over the eurozone.
Strong corporate results in the UK and US gave investor sentiment a boost, with Wall Street also enjoying gains as robust earnings from the likes of Kellogg saw the Dow Jones Industrial Average rise 0.8% in early session trading.
The more buoyant mood was helped by further signs that the UK economy might avoid a triple dip recession, with a purchasing managers' survey for the powerhouse services sector recording a return to growth in January.
And there was better news from Europe after a survey of the manufacturing and services sectors showed activity rose to a 10-month high in January across the 17-country eurozone.
A raft of economic releases in America added to the fightback, with data showing activity expanded in the US service sector and figures revealing a surge in house prices.
The positive services sector figures in the UK failed to help the pound as it continued its slide against the US dollar and euro. The pound fell to 1.56 dollars and 1.15 euros.
Among stocks in London, BP added 1% or 6.7p to 468.7p after it posted better-than-expected fourth quarter profits of $4 billion (£2.5 billion).
Arm Holdings, whose chip designs are used in Apple products, was also near the top of the risers board after it reported fourth quarter results ahead of market expectations. Shares were 39p higher at 931p, or 4%.
Banking shares were back in favour after losses on Monday following George Osborne's speech, which confirmed lenders would be threatened with break up if they did not adhere to new ring-fencing rules.
Barclays shares were 3.8p higher at 295.25p, despite upping its provision for redress relating to mis-sold payment protection insurance and interest rate hedging products by £1bn.
Royal Bank of Scotland was 8.9p higher at 337.5p as investors waited for news of its fine over the Libor rate-rigging scandal.
The biggest FTSE 100 risers were Hargreaves Lansdown up 40p to 734.5p, Eurasian Natural Resources ahead 14.9p to 344.2p, Arm Holdings 39p higher at 931p and BG Group up 38p at 1142p.
The biggest fallers were Smith & Nephew down 14p to 707.5p, Randgold Resources off 120p to 6155p, Antofagasta 14p lower at 1113p and Xstrata down 13.5p to 1150.