Significantly, officials repeated that warning Thursday - even though market expectations for a rate increase have advanced to around the middle of 2018.
Any more defections to that camp on Thursday would be liable to drive the currency higher although, with the economy struggling this year, most traders remain skeptical of the Bank's ability to raise rates at all.
"Clearly the Bank isn't overly concerned about yesterday's poor wage growth data, and sees the United Kingdom economy picking up more quickly than expected", said Hamish Muress, currency analyst at OFX.
A central plank of the Bank's attempts to kick-start the economy since the financial crisis has been to hold interest rates at record lows, cutting them again to their current rate of 0.25 per cent in the wake of June's vote to leave the European Union.
And recall, the Bank has a knack for not delivering on the "imminent" rate rises it has promised in the past.
BoE governor Mark Carney warned last month that this supply-side squeeze means interest rates may have to rise sooner than investors then expected.
The pound on Tuesday was moving closer to $1.33, where it hasn't traded since September 2016, according to FactSet data.
Above: We might finally be seeing a floor in the GBP/EUR established at the August lows.
The composition of the vote from the MPC is also likely to change, with the arrival of new member Sir Dave Ramsden taking the committee back to a full complement of nine members.
The unemployment rate in the United Kingdom fell in July to its lowest level in more than four decades, fueled by increasing participation in the labor force. But in recent months they have become increasingly concerned that subdued investment and feeble productivity growth is hurting the economy's capacity to produce goods and services without causing inflation.
The pound to euro rate rose by 0.25 per cent, this brings gains of 0.66 per cent of the last week however, sterling is still 6.3 per cent offside against the euro.
In the policy statement, the committee saw the potential for interest rates to increase within the next few months if the economy grows as expected and underlying price pressures rise.
Meanwhile, Brexit-fuelled inflation is set to climb above 3% in October - higher than the Bank previously expected.
But in a week when data showed United Kingdom prices rising faster and unemployment falling to a four-decade low, they said their tolerance for above-target inflation was lessening. "As such, the prospect of a series of rate hikes seems remote". Pay fell 0.4% when adjusted for inflation, which is now running just shy of 3%.
"Additionally, profit-taking may later see some correction in the rate".
"On balance we continue to see the pragmatists holding sway", said Sam Hill, senior United Kingdom economist at RBC Capital Markets, of the central bank rate-setters.