By Costas Pitas and Kate Holton

LONDON (Reuters) - British new car registrations fell for only the second time in more than four years in June and the number of shoppers on the country's high streets dropped 3.4 percent in the days following the shock vote to leave the European Union.

Investors will not know how the June 23 'Brexit' vote has impacted Britain's economy until official data becomes available next month, but early signs suggest it has hit consumer confidence.

Sterling is trading at 31-year lows and the Bank of England has warned that the financial risks it highlighted ahead of the vote are starting to crystallize.

The Society of Motor Manufacturers and Traders, a car industry body, said it was too early to link June's 0.8 percent year-on-year fall in sales to the referendum result. But it urged the government to boost economic confidence to avoid further drops.

Sales in June fell to 255,766 units, the SMMT said, only the second time they have dropped since February 2012. Registrations fell in October last year, blamed partly on a drop in sales of Volkswagen <VOWG_p.DE> models in the wake of the diesel emissions scandal.

On the high street, the number of people visiting British shops fell 3.4 percent in the 10 days following the referendum compared with last year, according to retail data company Springboard. It said the initial shock of the Brexit vote had put people off shopping.

That tallied with British retailer John Lewis <JLPLC.UL> which said on Tuesday that sales growth at its department store chain slowed in the week to July 2.

Online job site CV-Library said average salaries fell by 1.9 percent in June from the same month a year ago. However, it said advertised jobs jumped by 14.1 percent.

Britons had been warned by the government, the central bank and a wide range of economists that a vote to leave the world's largest trading bloc would damage the economy.

Bank of England Governor Mark Carney has said he expects the BoE to pump more stimulus into the economy over the summer and finance minister George Osborne has tried to reassure investors by holding out the prospect of further cuts to corporation tax.

The car industry, which hit record sales levels in 2015, had been one of the most vocal supporters of the campaign to stay in the bloc because of its export links to the continent.

Car deliveries typically occur several weeks after purchase decisions and most of June's sales happened before the June 23 vote, but there is normally a push by manufacturers at the end of each month to boost figures as much as possible, meaning the Brexit vote could have hit end-of-month registrations.

Ratings agency Fitch said on Tuesday that there will probably be a decline in British new vehicle sales due to slower economic growth and weaker consumer confidence.

Car sales hit a record high of 2.63 million in 2015 and the SMMT said last week it was not changing its forecast for a new record of around 2.7 million this year.

"It was always going to be ever more difficult for car sales to achieve year-on-year gains," said economist Howard Archer at IHS Global Insight. "However, it is very possible that there was some dampening effect on private and business car sales by heightened uncertainty in the run-up to the referendum."

(Additional reporting by William Schomberg; Editing by Mark Trevelyan)