Economists' expectations have shifted sharply in recent weeks to expect a top-up to the Bank's £200bn of asset purchases in either October or November, due to financial market turbulence and a stalling global economy.
Speaking to reporters after delivering a speech at Thomson Reuters' London headquarters, Broadbent said that he came close to voting to inject more stimulus into the economy this month.
"I can tell you I was reasonably close, so I don't think it would take much more of a deterioration. It depends exactly what you mean by deterioration. Some of these surveys, particularly of output in the euro zone, are consistent with there being (minimal) growth," he said.
Minutes of the Bank's last policy meeting showed it may be about to inject more stimulus into the economy, against a backdrop of financial market turbulence and rapidly slowing growth in major economies.
Broadbent said if the asset-buying programme was revived, it was likely that it would focus on buying UK government bonds, as it did first time around.
Business and consumer confidence has suffered in recent months from worries about unsustainable levels of government borrowing in the United States and the euro zone - particularly the fate of Greece, which is at risk of defaulting.
The euro zone debt situation was top of the agenda at this weekend's International Monetary Fund meeting. Although nothing concrete came of it, Broadbent said he was moderately encouraged by reports of the discussions.
"IMF meetings are not traditionally the place where those (big decisions) happen necessarily. I don't think we should have expected something very precise. In some ways, I was at the margin quite surprised and encouraged by getting what we did," he said.
But he also warned that markets were getting sceptical of policymakers' promises, and that the time had come for action rather than words.