By Dominic Lau

LONDON (Reuters) - The leading share index rallied 3.5 percent on Tuesday as banks led gains after a raised offer for Bear Stearns from JPMorgan Chase & Co soothed market jitters about the embattled financial sector.

The FTSE 100 closed up 193.9 points at 5,689.1, despite a gauge of U.S. consumer confidence taking an unexpectedly sharp hit and dropping to a five-year low in March. European shares also finished the day sharply higher.

"Given the low level of visibility that still exists and obviously the high level of volatility ... I don't think anybody can honestly say with their hand on their heart that we are over the worst," said Jeremy Batstone-Carr, head of private client research at Charles Stanley.

"Perhaps in the second quarter of the year investors will begin meaningfully to take on more risk in anticipation of the trough of U.S. economic activity," he said.

The UK benchmark index has shed nearly 12 percent so far this year on fears of a U.S. recession stemming from a meltdown in risky subprime mortgages, and is on track for its worst quarter since the third quarter of 2002 and its third straight quarter of losses.

Banks together added more than 54 points to the FTSE 100, with HBOS jumping almost 15 percent to lead the gainers' list. Barclays, Royal Bank of Scotland, Lloyds TSB, and Standard Chartered were up between 6.3 and 9.3 percent.

Financial shares were boosted after JPMorgan lifted its offer for Bear Stearns to $10 a share from $2, signalling that valuations in the sector had been thrashed excessively.

Insurers Standard Life and Old Mutual rose 7.6 and 8.6 percent, respectively.