King's remarks came as the central bank published its latest quarterly inflation report, suggesting the cost of living may rise to nearly 4 per cent this year.
The document forecasts that the Consumer Prices Index (CPI) will undershoot the Bank's 2 per cent target by the narrowest of margins in two years' time if borrowing costs remain unchanged at 5 per cent.
However, many analysts expect the Bank's monetary policy committee (MPC) to cut interest rates to 4.5 per cent, or lower, before the end of the year as the economy slows and house prices tumble.
Combined with soaring energy bills, food prices and dearer imports, that could force CPI to spike as high as 3.7 per cent, the Bank warned.
Figures released on Tuesday showed the inflation benchmark had jumped to 3 per cent in April from 2.5 per cent a month earlier, shattering City forecasts with its biggest monthly rise in almost six years.
King said: "As price increases feed through to household bills, they will lead to a squeeze on real take-home pay, which will slow consumer spending and output growth, perhaps sharply."
The Bank, which left interest rates unchanged this month, predicts economic growth could slow to just 1 per cent this year – below even the gloomiest of market estimates and against government forecasts of between 1.75 and 2.25 per cent.
Jonathan Loynes, chief European economist at Capital Economics, said a June cut in interest rates now looked "pretty unlikely" while any further loosening would be "modest in the foreseeable future".
He added: "The (inflation] report suggests that the MPC will not deliver the rate cuts which the news on the economy suggests are sorely needed."
Recent reports have seen a slowdown in the manufacturing and service sectors, record factory gate prices and falling house prices across much of the UK.
However, King played down the risk of a UK recession, saying: "We might get the odd quarter or two of negative growth but that is not in the central projection."
He said conditions in financial markets had improved since the introduction of a multi-billion-pound liquidity scheme, but "remained fragile".
Howard Archer, chief UK economist at Global Insight, said the inflation report made "pretty depressing reading" and highlighted the balancing act faced by the MPC.
He added: "The report further dampens already rapidly dwindling hopes that interest rates will be cut as soon as June."