By Andy Bruce and Peter Hobson

BIRMINGHAM, England (Reuters) - Bank of England Governor Mark Carney hit back at criticism from British Prime Minister Theresa May of the central bank's low interest rates, saying on Friday that he would not "take instruction" from politicians on how to do his job.

"Politicians have done a very good job of setting up the system," Carney said. "Where it can be difficult sometimes is if there are political comments on our policies as opposed to political comments on our objectives.

"The objectives are what are set by the politicians. The policies are done by technocrats," he told an audience in the city of Birmingham. "We are not going to take instruction on our policies from the political side."

May, promising to heed the protests of voters who decided to take Britain out of the European Union, took the unusual step last week of highlighting the "bad side-effects" for savers of the BoE's near-zero rates and said a change had to come.

The blunt words were among the most direct from a prime minister about the Bank since it won operational independence in 1997 and raised questions about political interference over the institution.

They also came as Carney, a Canadian, is due to announce in the coming weeks whether he plans to extend his five-year stay at the BoE, which is due to end in mid-2018, by a further three years.

Carney made his comments during a series of public meetings held by BoE officials to explain the work of the central bank.

Earlier on Friday, Carney gave a brief boost to the battered pound which has slumped in value since the Brexit vote in June, saying he was "not indifferent" to the level of sterling.

"We're not going to target the level, we're not going to have some magic number for it, but it does factor into our thinking," Carney said.

Sterling has fallen nearly 20 percent against the U.S. dollar since the referendum because of concerns among investors that Britain's economy will suffer from Brexit.

Carney also said he was willing to allow inflation to run "a bit" higher than the central bank's 2 percent target in order to help employment and allow Britain's economy to grow.

The BoE signalled in September it is likely to cut interest rates below their already historic low of 0.25 percent as soon as its next meeting in November in order to help the economy cope with the shock of the Brexit vote.

But since those signals from the Bank, the pound has extended its slump which is likely to further push up the price of imports and Britain's inflation rate.

Another BoE rate-setter, Kristin Forbes, said on Friday that inflation could "sharply" overshoot the BoE's 2 percent target, partly due to measures announced by the central bank in August to offset the impact of the Brexit vote.

Yields on 10-year British government bonds on Friday hit their highest level since the referendum on concerns about inflation.

(Additional reporting by David Milliken in Leicester and Helen Reid in Derby; Writing by William Schomberg; Editing by Jeremy Gaunt)