The Centre for Economics and Business Research (CEBR) says that the UK economy will slow from a growth rate of 2% this year to just 1.3% in 2002.
And it says that the US economy will record a zero growth rate this year, before recovering to 1.4% in 2002.
Overall, the effect of the terrorist attack will be to reduce the total output of the UK economy by some £13bn, and the total output of the world economy by $680bn (£440bn), it forecasts.
"Although the outlook is highly uncertain, we are clear that in the short term the world economy has been dealt a blow which will depress world growth for at least nine months," said Doug McWilliams, the head of CEBR.
Rate cuts
Mr McWilliams said that the outcome could be even worse, as he was assuming in his forecast that there are no further terrorist attacks, that expected reprisals by the US do "not destabilise the world economy further", and public spending in the US is increased in response to the disaster.
Already central banks around the world have been responding to the more pessimistic climate by cutting interest rates.
Last week there were a co-ordinated series of rate cuts in the US, Europe and the UK.
And speaking to the BBC on Sunday, the governor of the Bank of England, Sir Edward George, said that he expected "to see some weakening in the current quarter and perhaps in the next quarter for the UK economy."
He did not rule out further rate cuts if necessary following the 0.25% cut last Tuesday which brought UK interest rates to 4.75%, their lowest in decades.
Mr McWilliams is forecasting that UK interest rates will fall to 3.5% by early next year.
Interest rates in the US are already at 3% and expected to fall further.
Growing pessimism
Many economists believe that the terrorist attacks could not have come at a worse time, with growth in the US - the engine of world economic growth - already slowing down dramatically after eight years of economic boom.
The financier George Soros said he thought that the coming US slump would be "steeper, deeper, but hopefully shorter" than previously predicted.
Although some economists are predicting a mild recovery in the US, most expect the knock-on effects on Europe and Asia to be severe.
The slowdown could become more severe if stock markets fall further, and that affects consumer confidence, which is already fragile.