A bounceback for US shares, a further recovery in China and a stellar performance by Japanese shares helped the benchmark FTSE 100 index to close 82.91 points or 1.35% up at 6,229.01.
Revised growth figures for the eurozone on Tuesday also underpinned confidence.
Ryanair was a strong performer, up 5.2%, after it said profits would be 25% higher than thought.
Broker Hargreaves Lansdown's shares were up 7% after its results and Barratt Developments shares were 0.2% higher after an initial 2% rise. It earlier reported profits up 45%.
Foxtons estate agents were another good gainer, rising 3.75% after an upgrade.
On the currency markets, the pound was down 0.2% against the dollar at $1.5366 but was up 0.2% against the euro to â‚¬1.3774.

The 26-year-old was injured in last week's win over Exeter.
Director of rugby Richard Cockerill told BBC Radio Leicester: "With eight weeks of the season to go that is probably the last we will see of him."
Meanwhile, scrum-half Sam Harrison, 24, has signed a new deal, but the length of the contract has not been revealed.
Benjamin has been plagued by injuries since signing from Worcester in 2012, suffering a serious neck injury which delayed his first-team debut by 15 months.
He also sustained a knee injury that ruled him out for four months last term.
But Cockerill said: "It is certainly not too serious and he will make a full recovery in the next eight to 10 weeks."

Police found the child after being called to at a home at Bromsgrove Cottages in Faringdon at around 13:20 GMT on Tuesday.
A 40-year-old woman has been arrested on suspicion of murder and the child's next-of-kin have been informed.
The boy was said to be of primary school age. Police have increased their presence in the area.
They said this was in order "to provide reassurance".
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Supt Rory Freeman, local police area commander for South and Vale of White Horse, said: "This is a very shocking discovery and I am aware it may have a very direct impact on the community of Faringdon.
"We would advise any members of the community affected by this incident to speak to one of the neighbourhood policing team."
The woman remains in police custody. Anyone with information is asked to call 101 quoting 730.
Police tape remains around the line of cottages, and uniformed and plain clothes officers are coming and going as the investigation continues.
News that something serious had happened spread rapidly on social media on Tuesday night.
This morning passers-by are saying they are shocked and saddened by what's happened.
One lady walking to school with her son stopped to give a rose to one of the police officers monitoring the cordon.
This is quite a visible place opposite the fire station; a lot of people go past here, so the police are asking anyone with information to contact them.
(Close): London's leading shares ended the day in positive territory as global investors regained confidence.
[NEXT_CONCEPT]
Leicester Tigers winger Miles Benjamin is likely to be out for the rest of the season because of a knee injury, reports BBC Radio Leicester.
[NEXT_CONCEPT]
A murder investigation has been launched after a boy was found dead at a house in Oxfordshire.