* FTSE down 0.4 percent, traders eye possible correction
* Banks wane as eurzone fears rumble on
* Integrated oils lower with crude
By David Brett
LONDON, Dec 30 (Reuters) - Britain's top share index fell on Thursday, drifting away from the 6,000 level in thin volumes on the last full trading session of 2010, pulled down by banks and energy stocks.
The FTSE 100 index closed down 25.35 points, or 0.4 percent, at 5,971.01, having lost 0.2 percent on Wednesday.
Trading volume was 30 percent of the 90-day moving average.
"(Lack of volume) is leading some longer-term traders to suggest that a more serious correction is imminent once large traders and institutions return after the New Year's holiday," said James A. Hyerczyk, analyst at Autochartist.
"The big picture range of 5519.19 to 6021.46 projects a possible major correction to 5770.33 to 5711.06."
Banks were lower, with global lender HSBC, down 0.7 percent, and Lloyds Banking Group off 1.0 percent, weighed on by worries over euro zone debt exposure.
The sector has gained just 1.2 percent in 2010, well below the 23 percent banks gained in 2009, albeit from a low base, as investors' concerns have grown over economic stability within the euro zone.
Investors shrugged off upbeat data from the United States, which boosted recovery hopes.
New U.S. claims for jobless aid hit their lowest level in more than two years last week, and factory activity in the Midwest grew in December at its fastest pace since 1988, evidence that the recovery has gained steam.
ENERGY DRAIN
Weakness in integrated oils was also a drag on blue-chip sentiment, with the sector falling back after recent gains as the crude price slipped back below $91 a barrel.
BG Group fell 0.9 percent.
Miners provided the main underlying prop for blue chips as a weaker dollar helped again to boost metal prices.
Mexican silver miner Fresnillo was the top FTSE 100 riser, up 2.6 percent as the price of the metal hit a 30-year peak.
Record copper prices also helped lift Rio Tinto 0.7 percent.
But gold miners Randgold Resources and African Barrick Gold shed 2.4 and 1.2 percent, respectively, having posted strong gains in the previous session.
The FTSE 100 index is up 8 percent on the month, the strongest December performance since 1987, when it rose 8.5 percent.
The blue-chip index is up 10.3 percent this year and has gained 25 percent since it touched the year's low at the start of July.
"There is every chance that there could be a small correction into the new year as prices normalise with the return of normal market volumes, but if the FTSE can ... (remain) above the 5,900, there is every chance the rally may continue into the new year," said Joshua Raymond, market strategist at City Index. (Editing by Will Waterman)