By Andy Bruce

LONDON (Reuters) - The Bank of England's top two monetary policymakers said interest rates may need to fall further, as surveys on Friday sustained their view that even a "sledgehammer" stimulus will not be enough to fully counter a post-Brexit vote slowdown.

Ben Broadbent, the BoE's deputy governor for monetary policy, told Reuters he would support reducing interest rates again, while his boss Mark Carney repeated that rates could fall further if needed.

Their comments follow Thursday's rate cut to a new record low of 0.25 percent and the launch of stimulus measures worth up to 170 billion pounds - a huge package designed to offset the shock from June's vote by Britons to leave the European Union.

"There was a majority that expected to vote to cut interest rates again, were the economy to unfold in line with forecasts, and yes, I was one," Broadbent said in an interview at the BoE, which was also attended by two other news organizations.

Despite the scope of the new stimulus plan, Carney again emphasized that the number of unemployed was likely to rise by around a quarter of a million in the next few years, in an interview with LBC radio.

A closely-watched survey of recruitment firms offered an early sign the BoE might be right, while carmaker Nissan raised doubts about its long-term investment plans for Britain.

The labor market entered "freefall" after the vote to leave the EU, with the number of permanent jobs placed by recruitment firms last month falling at the fastest pace since May 2009, according to the Recruitment and Employment Confederation.

"The Treasury pay attention to this survey - (it) has a good record of predicting the labor market. They will be worried," Rupert Harrison, chief macro strategist for multi-asset at BlackRock who was chief of staff to ex-finance minister George Osborne, said on Twitter.

Most economists agreed on Thursday that the Bank of England's stimulus will need to be bolstered by reforms and significant investment from the government to truly counter the downturn resulting from the vote to leave the EU.

But Broadbent warned no conventional monetary or fiscal tools could fully compensate for the deep structural changes to Britain's economy caused by leaving the EU.

"There are limits to what monetary policy, indeed any demand management policy can do - conventional fiscal policy as well - to offset what is a structural effect on the economy," he said.

Reflecting doubt about Britain's future as a trading power, Nissan's <7201.T> chief executive warned investment decisions in Britain would hinge on the terms of a Brexit deal with the EU.

"The question is what's going to happen in terms of customs, what's going to happen in terms of trade, what's going to happen in terms of circulation, particularly of the products," Renault-Nissan Alliance Chief Executive Carlos Ghosn told the BBC.

"All of these are very sensitive elements that are going to determine, how and how much we are going to invest in the UK, particularly for the European market."

The outlook for Britain's housing market is also uncertain.

A survey from mortgage lender Halifax showed British house prices fell in July, reversing gains seen the month before, but it is too soon to tell if Britain's vote to leave the European Union will have a major impact on the housing market.

(Editing by Michael Holden and Richard Balmforth)