Surging oil and commodity prices combined with this year's rise in value added tax propelled British inflation to 4 percent in January -- double the BoE's target -- but the Bank does not seem in any hurry to raise rates from the current 0.5 percent.
Indeed, inflation in Britain has been above target for most of the last five years, leading some economists to question the BoE's inflation-fighting zeal and the validity of the consumer price inflation target.
Last week's inflation data obliged King to write an explanatory letter to the government -- his tenth in almost four years -- but Osborne said he saw no case for altering the 2 percent target.
"I think the inflation regime, the remit, is the correct one. I've got absolutely no thoughts or plans about changing it," Osborne told reporters after a meeting of G20 finance ministers in Paris at the weekend.
"And as my exchange of letters with the Governor confirmed, I'm happy with the approach they're taking and I trust the judgement of the Monetary Policy Committee."
BALANCING ACT
BoE policymakers face the dilemma of how to bring inflation back on track over the medium term without throwing the fragile economic recovery off course.
Their job has been complicated by the goverment's rise in VAT, which is likely to propel inflation to almost 5 percent in the coming months, while public spending cuts that will start to take effect this year are likely to dampen economic growth.
Osborne batted away criticism that the government's austerity measures were making the BoE's task more difficult and said the cuts would give the central bank "space" to keep interest rates lower for longer.
"Any monetary authority with the competence of the Bank of England can see through temporary increases in price levels and look to permanent threats to inflation," he said.
Indeed, BoE forecasts published last week showed it expects inflation to fall to below target at the two-year horizon on which it bases monetary policy decisions, on the assumption that interest rates rise gradually this year.
At the same time, King repeated his support for the government's austerity measures, saying it needed a "Plan A" for reducing a record peacetime deficit, and drawing a rare attack from Labour finance spokesman Ed Balls who accused him of putting the BoE's independence at risk.
Osborne said Balls' attack was "flimsy" and "immature".
"I think the Bank of England has credibility. I certainly have complete confidence in it. I don't think it's being political or partisan," he said.
"What I think is important is that the British government does its job correctly, which is to get a control of fiscal policy and put in place the long-term changes to improve our economy and the short term improvements we can make as well. And the Bank of England does its job -- which I think it's doing competently -- which is to meet its inflation mandate. That's how we divide up the responsibilities."