* Carney sees domestic inflation picking up
* Sterling jumps, gilts fall
* BoE's Miles: rate hike "clearly is coming"
* No big impact see from new minimum wage (Adds comments on productivity, writes through)
By David Milliken and William Schomberg
LONDON, July 14 (Reuters) - Bank of England Governor Mark Carney said on Tuesday that the time for a first British interest rate hike since the financial crisis was getting closer as economic recovery gathers momentum.
Speaking to British lawmakers for the first time since May's national election, Carney said households should start to prepare for higher borrowing costs, though the central bank would only raise rates slowly.
"The point at which interest rates may begin to rise is moving closer with the performance of the economy, consistent growth above trend, a firming in domestic costs, counter-balanced somewhat by disinflation imported from abroad," Carney told a parliamentary committee.
Carney has been saying that a rate rise is getting closer for more than a year, and on Tuesday he said there would inevitably be "shocks and adjustments" ahead. But investors reacted to his comments -- the first on monetary policy since May -- by pushing up the pound and selling government bonds.
British gilt futures fell nearly 30 ticks from their level before Carney's comments, but then pared most of those losses. Yields on 30-year gilts rose to close to an eight-month peak.
Sterling jumped by more than a cent against the U.S. dollar .
Carney said the strengthening in sterling against other currencies was helping to keep inflation low but was not the dominant factor for the outlook for prices.
Earlier on Tuesday, official data showed Britain's inflation rate fell back to zero in June.
The BoE has held rates at a record low of 0.5 percent for more than six years. Investors mostly expect a first rate hike in mid-2016, although economists have said it is likely to happen earlier in the year.
Carney also repeated his view that British interest rates would not rise to their levels before the financial crisis.
"I do think there are a variety of factors that mean that the new normal, certainly over the policy horizon over the next three years, is substantially lower than it was previously," he told parliament's Treasury Committee. "I see no scenario in which they would move towards historic levels."
Another rate-setter at the Bank, David Miles, said the first rise in borrowing costs "clearly is coming" and it was "not a bad thing". Miles has been one of the Bank's nine monetary policy makers who has voted most consistently to support the economy with low interest rates and additional stimulus.
Carney said a new higher minimum wage announced by finance minister George Osborne last week would probably give a small boost to Britain's weak productivity record as companies shifted more towards investment rather than hiring.
He said he noted the view of Britain's official budget forecasters that the inflationary impact of the new minimum wage would be "very modest". (Additional reporting by Andy Bruce, James Davey, Neil Maidment and Kate Holton; writing by William Schomberg; editing by Hugh Lawson/Ruth Pitchford)