(Watch: When will the sterling rally end?)
He also cautioned against getting "too hung up" about exactly when the central bank will raise interest rates from their record low 0.5 percent, after financial markets and other policymakers pointed to spring 2015 as a possibility.
In a speech to local businesses in Darlington, northeast England, Bean said there were clear signs Britain's economy was on the mend, but that it was "early days" and the trade deficit needed to narrow to put growth on a more solid footing.
"Any further appreciation of sterling, which has risen almost 10 percent in trade-weighted terms since March, would not be particularly helpful in terms of facilitating a rebalancing towards net exports," Bean said.
In a question and answer session after his speech, he said a stronger sterling would could reduce inflation because of weaker import prices.
"We would be more likely to undershoot the inflation target in the medium term, and that would mean we would need to keep policy looser for longer than would otherwise be the case."
Last month Ian McCafferty, who sits alongside Bean on the BoE's rate-setting Monetary Policy Committee, also said further sterling strength would be a worry and could potentially make the bank delay raising interest rates.
Bean said British exports had been somewhat disappointing - especially in the services sector - although he said there were some more positive stories of businesses bringing back activities that had previously moved offshore.
Don't get hung up on hike
Bean also warned against pinpointing spring 2015 as the date when the BoE would raise interest rates.
"(The) market curve implies a first rise in Bank Rate in the spring of 2015, though I should stress that we are likely to learn a lot between now and then about the pace of the recovery, the amount of slack and the evolution of supply, and the impact on costs and prices," he said.
(Read more: BoE's Carney braced for grilling in forex probe)
"So I would counsel against getting too hung up about the precise date at which Bank Rate first rises."
McCafferty and fellow MPC member Martin Weale had both cited spring 2015 as
a possibility for the first rate hike in recent interviews.
Bean said that when the Bank does raise interest rates it will do so gradually, and that rates are likely to remain below their pre-crisis average of around 5 percent "for some time" - perhaps around 2-3 percent, echoing the new forward guidance given by Governor Mark Carney last month.
But Bean did not go quite as far as MPC member David Miles, who last month suggested the "new normal" for monetary policy would be interest rates averaging below pre-crisis levels.
Bean said it was possible the BoE might not sell back all of the 375 billion pounds ($627 billion) of gilts which it bought under its quantitative easing stimulus scheme. Because banks might want to park more reserves at the BoE due to tighter regulation after the financial crisis, the BoE might need to hold more gilts as a counterparty.
"We may not be in a position to sell all of the gilts back, and some of them will of course roll over naturally," Bean said. The BoE has said it will reinvest the proceeds of maturing gilts while interest rates remain at 0.5 percent, but has not said what it will do after that.
MPC member David Miles also made the point in a speech last month that the BoE might need to hold on to government bonds as collateral for banks' reserves.
Bean said that although Britain's economic recovery has so far been driven by household consumption and housing market activity, there were reasonable grounds to believe business investment would take over as a major driver for the recovery.
He also said there was more scope for housing investment to continue driving growth, although perhaps only a little room for the household savings ratio to drop further as consumers save less as a proportion of their income.
The BoE's Financial Policy Committee was keeping a "beady eye" on the housing market, he added.
"(There) is a risk that increased demand for housing ends up mainly in higher house prices rather than more houses. If associated with excessive expansion in mortgage lending, that may create future financial stability risks."
(Read more: Five years on: what 0.5% rate has meant for the UK)
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