The FTSE 100 closed up 1.62% at 6,032.24 points.
The index had fallen 2.8% in the previous session after commodity-related shares were hit by worries over global growth prospects.
However, investors shrugged off another survey suggesting China's manufacturing sector was continuing to contract.
A similar survey for the eurozone indicated that activity among businesses in the bloc continued to expand this month, although at a slower rate than in August.
The preliminary reading of the Markit purchasing managers' index (PMI) for the eurozone was 53.9 in September, down from 54.3 last month. A reading above 50 indicates expansion.
British Airways owner IAG topped the FTSE 100 risers board, closing up 4.7% to 594p after Morgan Stanley raised its price target for the stock. The news lifted shares in Easyjet, which ended the day 3.4% higher.
Energy stocks were bolstered as the price of oil steadied. Shares in BP ended the day up 1.3%.
Shares in Smiths Group ended up almost 1% after the company reported full-year results and said Andrew Reynolds Smith would take over as chief executive from Friday.
In the 12 months to 31 July, revenues at the engineering group dropped 2% to £2.89bn, but pre-tax profits rose 3% to £459m.
Drinks giant Diageo closed higher by 0.96%. The company said that recent currency fluctuations would cut operating profits by about £150m, but added that the financial year had begun well and "performance is in line with our expectations".
United Utilities shares closed the day 1.48% higher, after the water firm's latest trading update. The company said its profits would be hit by about £25m after it had to pay compensation to about 300,000 households in Lancashire following the discovery of a parasitic bug in water supplies.
On the currency markets, the pound fell 0.81% against the dollar to $1.5242, and dropped 1.09% against the euro to €1.3657.
(Close): UK shares closed higher, recovering some ground lost on Tuesday, despite further signs of weakness in China's manufacturing sector.