Gross domestic product will fall 0.1pc in the three months through December, according to a survey of economists.
Last month, the same economists said the economy would expand slightly. While economists see 0.2pc expansion in the first quarter of 2013, the odds of the economy slipping back into a recession within the next year increased to 33pc from 28pc.
The health of the British economy is vital to tens of thousands of Irish companies which export goods and services to our nearest neighbour.
While the central bank halted bond purchases last week, Mr King said policy makers hadn't ruled out restarting their quantitative-easing programme again if needed.
"With business surveys and an external environment still weak, there's a pretty high chance that GDP will fall back in the fourth quarter," said Samuel Tombs, an economist at Capital Economics Ltd.
While Britain's economy exited a double-dip recession in the third quarter, its first since the 1970s, the rebound was partly attributable to the Olympics. That followed a second-quarter slump exacerbated by an extra public holiday in June.
The Office for National Statistics has quarterly GDP data going back to 1955.
On Thursday, new figures showed that retail sales fell more than forecast in October, while manufacturing and services surveys weakened. Mr King said a "zig-zag pattern" of output was likely to continue.
Mr King said that the euro-area debt crisis remained the biggest risk to the UK. He made his comments as the Bank of England published its quarterly Inflation Report, which also highlighted pressure on the economy from Chancellor of the Exchequer George Osborne's budget cuts. (Bloomberg)