* UK mortgage approvals highest since Jan 2008 in Nov - BoE
* Lending to businesses suffers biggest fall since 2011
* Nationwide reports fastest rise in house prices in 4 years
* Construction PMI second-strongest in six years
LONDON, Jan 3 (Reuters) - Britain's booming construction industry and fast-rising house prices suggest the economy finished 2013 on a high but a sharp fall in business lending raises doubts about how sustainable the recovery will prove.
Friday's lending, housing market and construction figures from the Bank of England, major mortgage lender Nationwide and data company Markit were all strong, as were Christmas sales numbers from big clothing retailer Next.
However, the central bank and other economists say Britain needs more exports and business investment to fortify growth in 2014 and shake off a dependence on consumers saving less and spending more.
Britain's economy grew at an annualised rate of more than 3 percent in the second and third quarters of 2013, and strong fourth-quarter data could lead to the fastest full-year growth since 2007 - something quite unexpected earlier in the year.
But while the central bank on Friday showed mortgage approvals in November were their highest since January 2008 - though still well below pre-crisis levels - net lending to businesses took its biggest fall since comparable figures began in May 2011.
"Overall the picture from the data today remains consistent with a UK recovery that has been fairly household-led," said David Tinsley, UK economist at French bank BNP Paribas. "We would look for that to change in 2014, but a risk remains that corporates will remain reluctant to borrow and invest."
Britain's housing market has been bolstered by falling unemployment, low interest rates and government programmes to make mortgages cheaper and easier to obtain.
This in turn has lifted confidence in the construction industry, with Markit's survey of purchasing managers showing only a slight slowdown in growth in December from November's rate, which was the fastest since August 2007. Housing was the strongest sector, though commercial projects picked up too.
Manufacturing data released on Thursday was also robust, and a closely watched services survey due on Monday is forecast to show sustained strength.
RISING HOUSE PRICES
Outright levels of construction remain low, however, and Nationwide said the supply of new homes was not keeping up with demand - contributing to an 8.4 percent annual rise in house prices, the biggest since June 2010.
Prices rose 1.4 percent in December alone, the biggest one-month jump in over four years and prices in London and Manchester are up 15 and 20 percent respectively on the year.
At a national level, house prices are still 5 percent below their pre-crisis peak. But this news is likely to concern critics who fear programmes such as the recently-expanded Help to Buy scheme - which led to an extra 6,000 mortgage applications between October and December - are more likely to pump up house prices than spur the building of more homes.
Bank of England Governor Mark Carney has warned that Britain's housing market has the tendency to rapidly overheat, and in November the central bank reined back a scheme that offers cheap finance to banks, saying it will only help those seeking to lend more to businesses.
The BoE is due to review Help to Buy in September, but Carney has said it could make recommendations sooner if it felt the scheme threatened financial stability.
Underlining the risks, Friday's data showed mortgage approvals in November rose more than expected to 70,758 from around 54,000 at the start of 2013, though below pre-crisis averages of more than 90,000.
Business lending fell by 4.7 billion pounds ($7.73 billion) and is almost 4 percent down on the year.
The BoE had no immediate explanation for the record fall, other than that it was concentrated in larger firms. Lending to small businesses rose by 140 million pounds.
Greater numbers of mortgage approvals - and subsequent house purchases - have historically boosted economic confidence in Britain and led to greater consumer demand.
However the management of Next, which revised up sales forecasts on Friday, noted that wage rises still lag inflation and spending growth has been funded by lower household saving.
"Any return to significant economic growth is likely to result in rising interest rates which, in turn, is likely to moderate spending of those with mortgages," it said in a trading statement that was stronger than most of its rivals'.
With British output 2 percent below its pre-crisis peak - lagging almost all other big advanced economies - the BoE has committed to keep interest rates at a record low until unemployment falls to 7 percent.
The jobless rate has fallen much faster than the BoE forecast in August, meaning 7 percent could be reached as soon as the end of 2014.
However, the central bank has stressed that whether interest rates rise will hinge on medium-term inflation pressures such as labour productivity.