LONDON (Reuters) - Britain's business minister Sajid Javid said the government should cut corporate and personal taxes to soften the blow from an expected slowdown after Britain's vote to leave the European Union.

Javid told the Financial Times the government needed to switch its focus from reducing the deficit to stimulating economic growth by introducing unfunded tax cuts to boost research and investment for companies.

Confidence in Britain's economy has been rocked by the decision by voters to leave the world's largest trading bloc on June 23. The pound is trading at 31-year lows and the Bank of England has warned that the financial risks it highlighted ahead of the vote were starting to crystallize.

Finance minister George Osborne has said he plans to cut Britain's corporation tax to below 15 percent and has also dropped his aim of turning Britain's budget deficit into a surplus by 2020.

Javid backed Osborne's softer approach to fixing the public finances. He told the FT it was hard to predict what would happen to the deficit.

"Does it mean 3 percent becomes 4 percent or 5 percent? I don't think anyone can say at this point," he said.

Britain's budget deficit was just under 4 percent of gross domestic product in the financial year which ended in March.

Javid said the government should double tax credits for research and development, exempt new plant and machinery from business rates and increase the annual investment allowance. He said the threshold at which people start paying income tax should also rise by 1,000 pounds.

As well as the signals from the government of help for the economy from lower taxes, Bank of England Governor Mark Carney has said he expects the central bank to provide more monetary stimulus over the summer. On Tuesday, the BoE lowered a requirement for banks to set aside money to cover losses.

It is not clear how long Osborne and Javid will remain in their jobs. Prime Minister David Cameron has said he will resign by September and the ruling Conservative Party is in the process of choosing a new leader.

(Reporting by Kate Holton, editing by William Schomberg and Estelle Shirbon)