It comes after the Bank dropped the forecast from 0.8% three months ago and 2% a year ago.
The Bank of England also slashed its forecast for medium-term growth from 2.8% to 2.1%.
Speaking on the Bank’s latest quarterly inflation report published today King said the UK is “navigating rough waters and storm clouds continue to roll in from the euro area”.
He did suggest inflation would continue to fall and hoped there would be a “gradual recovery in output” in the longer term however.
Output has contracted in each of the past three quarters but King said the underlying picture is probably not as weak as the headline data suggest.
The extra bank holiday in June is likely to have reduced output in Q2 by around 0.5%, an effect that he said should unwind in Q3.
And he said a large fall in construction output in the first half of the year, which seems at odds with survey data, is unlikely to be repeated.
King said: “Even looking through these erratic factors the underlying picture is that output has been at best broadly flat over the past two years, and has continually disappointed expectations of a recovery.”
Private sector employment has grown robustly and unemployment has edged downwards.
Although King said this was “welcome news in its own right” the resilience of employment combined with the weakness of output, means that productivity growth has been unusually low.
That continues a recent pattern of both weak output and productivity growth that is “difficult to explain”.
King warned: “We cannot be sure how persistent that weakness will be, and that is one reason why the Committee has lowered its forecast for growth.”
“A major concern for the Committee in recent months has been the rise in bank funding costs, related to the euro-area crisis, which has fed through into higher rates for domestic borrowers.”
The new Funding for Lending Scheme, a joint Bank of England and Treasury initiative, was designed to reduce those pressures.
The Scheme provides incentives to banks and building societies to lend more to UK households and businesses. The design takes into account that, before the Scheme, a number of large banks planned to reduce their lending to the real economy.
The Funding for Lending Scheme is bigger and bolder than any initiative so far tried to get the banks lending again. Although its overall impact is uncertain, the early indications are positive, with some banks cutting their loan rates.
CPI inflation has continued to fall from its high of 5.2% last September, reaching 2.4% in June, and is expected to fall further this year.
Twice in the past four years inflation has risen above 5% as a result of external price pressures.
King said: “Unlike the Olympians who have thrilled us over the past fortnight, our economy has not yet reached full fitness. But it is slowly healing.
“Many of the conditions necessary for a recovery are in place, and the MPC will continue to do all it can to bring about that recovery. As I have said many times, the recovery and rebalancing of our economy will be a long, slow process.
“It is to our Olympic team that we should look for inspiration. They have shown us the importance of total commitment when trying to achieve a goal that may lie some years ahead.”