Significantly, he added that Bank was not excessively concerned about the level of British households' debt, as the ratio of consumer credit to incomes continued to be much lower than before the financial crisis.
Today the Bank voted to keep rates at 0.25 per cent, by a margin of six votes to two. "Some tightening of monetary policy would be required to achieve a sustainable return of inflation to the target".
Jake Trask, FX research director at OFX, added:"Sterling tanked as the BoE chose to hold interest rates".
The Bank of England chose to keep rates unchanged at all-time lows as it completed its two-day meeting today.
Mr Broadbent said there should not be undue concern following a rate raise.
The pound fell 0.7 per cent to US$1.3132 in early-afternoon trading as the prospect of slower economic growth damped expectations for a rate increase in the next few months.
The Bank of England has also cut its economic growth forecast for both 2017 and 2018.
His wary tone about Brexit prompted an angry response from a leading supporter of last year's Leave campaign.
But he said the United Kingdom was "a little bit" better placed to cope with an interest rate rise.
The BOE's latest forecasts for the economy are based on a smooth Brexit, though Carney said on Thursday that the assumption will be tested. We have the United Kingdom inflation hearings and also the BOE rate announcement and statement as well. It expects growth of 1.7% this year, down from its previous prediction of 1.9%.
At its simplest level, the policy dilemma facing Britain's central bank is that it must balance surging inflation brought on by the weakened pound since the referendum with the slowdown in the economy, dwindling consumer spending, and declining inward investment. However, it has signalled the end of the Term Funding Scheme, created to make cheap money available to banks.
A series of surveys of Britain's manufacturing, construction and services sectors published this week suggested the economy remained in a low gear in July.
The BOE has revised down its 2017 growth projections, to 1.7 percent from 1.9 percent in May, saying the United Kingdom economy will remain "sluggish".
The government sets the Bank an inflation target of 2% but the rate is now above that at 2.6%, with policymakers expecting it to pick up and peak around 3% in the autumn on the consumer prices index (CPI) measure.
He points out that savers have not only seen little to zero gains on their cash, but also an uptick in inflation, which hit a four-year high of 2.9 per cent in May and is expected to peak to 3 per cent in October.