"In the last six weeks... I am very struck by how much has changed since we produced our May Inflation Report," King told parliament's Treasury Committee.
"I am pessimistic (about the Eurozone outlook). I am particularly concerned because over two years now we have seen the situation in the euro area get worse and the problem being pushed down the road," he said.
Britain's economy slipped into its second recession since the start of the financial crisis around the turn of the year and fears of a longer slump have been rising as companies hold back investment and exports suffer from the euro zone crisis.
The central bank's Monetary Policy Committee voted 5-4 against buying more government bonds with newly created money to boost the economy, but most economists expect another round of quantitative easing in July.
The government and the central bank announced two schemes on 14 June get credit flowing through the economy by lowering banks' funding costs.
Policymakers Ben Broadbent and Spencer Dale - who both voted against more stimulus in June - as well as David Miles all indentified the Eurozone debt crisis as the main threat to Britain's economy in their annual reports to parliament.