Expectations of a rate rise are at their lowest level since the height of the financial crisis, according to a survey by the Bank taken shortly after Mr Carney unveiled its new "forward guidance policy".
The figures, which also showed that members of the public on average believe inflation to be falling, will give some comfort to the new governor following his pledge on interest rates which is designed to support the fledgling recovery.
Mr Carney has been at pains to press home the impact of the low-rates policy amid hopes it will give confidence to individuals and businesses planning to invest.
He announced at the start of last month that, subject to inflation remaining under control, the Bank rate would not rise from its historic low of 0.5% until the unemployment rate had fallen to 7%, representing around 750,000 new jobs.
Bank forecasts on unemployment suggested this would not happen until 2016 at the earliest but traders have poured cold water on this timetable, pushing up market interest rates and blunting the impact of the guidance.
Meanwhile, on average the public believed inflation had risen by 4% in the last 12 months, compared with 4.5% in May. They believed it would be 3.2% over the coming year, compared with 3.6% in the previous survey.
The figure is some way above the official measure of consumer price inflation at 2.8% but the fact that expectations are falling is important because public perceptions of the direction of inflation underpin the Bank's forward guidance policy.
A key caveat or "knockout" built into the policy states that the unemployment threshold for keeping rates low would no longer hold if medium term inflation expectations "no longer remain sufficiently well-anchored".
The fact that inflation expectations are coming down suggests it is more likely the knockout is not activated - and therefore low interest rates will remain in place.
It is these "knockouts", as well as the belief that the Bank's unemployment forecasts have been too pessimistic, which have fuelled market doubts about the forward guidance timetable, with many believing rates will go up a year earlier than it implies.
This expectation of an earlier interest rate rise has pushed up bond yields - the rate the Government pays to borrow money, which can filter through to higher borrowing costs in the real economy despite the Bank rate staying low.
The latest survey will cheer Mr Carney after his efforts to go over the heads of the City to press home the impact of forward guidance.
In a speech to business leaders in Nottingham last week he stressed that loans to households and businesses were largely determined by the rate set by the Bank rather than those determined by the financial markets.
Howard Archer, economist at IHS Global Insight, said the new figures represented a "double dose of good news for Mark Carney".
"This suggests that the Bank of England's new forward guidance policy indicating that interest rates are unlikely to rise before mid-2016 is being believed more by consumers than it is by the markets," he said.
The latest figures are based on a survey of 2,050 people by GfK NOP between 8 and 13 August. The Bank's forward guidance policy was announced on August 7.
© 2013 Press Association