By Matt Falloon and Sumeet Desai

LONDON (Reuters) - House prices suffered their steepest annual fall in 15 years in April, stoking fears of a deep downturn, as figures showed more than 25,000 people succumbed to bad debt in the first three months of the year.

A pick up in the number of companies going bust will also add to growing concerns over the state of the economy and exacerbate the challenge facing Prime Minister Gordon Brown as Labour slumps to defeat in local government elections.

Brown must now win back the confidence of voters before he has to call a national election by May 2010.

The weak housing market figures from Britain's biggest mortgage lender HBOS come after a Bank of England policymaker warned prices could fall by a third. They have already declined more than 5 percent from last August's peak of an average 199,600 pounds.

"This is a dark cloud that is getting ever darker for the economy," said Alan Clarke, an economist at BNP Paribas.

House prices fell 1.3 percent on the month to an average 189,027 pounds last month, HBOS said, the third monthly decline in a row and leaving prices 3.7 percent lower than April last year.

That was the biggest yearly decline since June 1993, analysts said, when Britain was still in the throes of a protracted housing slump.

"What is most concerning is that these house price falls have come with the economy only having registered a modest slowdown," said Seema Shah, a Capital Economics property expert.