The FTSE 100 index closed 1.8% higher at 6,902.2 points, with miners Rio Tinto and Anglo American the top gainers.
Banks were boosted by hopes that a rescue package for Italy's Monte Dei Paschi may emerge.
Reuters reported that Italy was preparing to take a â‚¬2bn stake in the country's oldest bank.
"There is general Christmas cheer in the markets after the Dow Jones struck another record high on Tuesday," said Kathleen Brooks from City Index.
"This is helping to boost risk sentiment overall. The markets are still banking on a big US [growth] upswing under Trump, and also more stimulus from the ECB, which leaves equity markets in a sweet spot as we head into the end of the year," she added.
Shire was the biggest faller, down 4.5%, with WPP shedding 2.8%.
On the currency markets, the pound fell 0.55% against the dollar to $1.2608, and dropped 0.9% against the euro to â‚¬1.1723.
That followed a surprise fall in UK manufacturing, which analysts said could dent fourth quarter growth figures.
London's main share index rose on Wednesday, lifted by shares in miners and banks.