Policymakers voted 8-1 to hold rates and the Bank said the outlook for inflation was "muted".
The pound fell more than a cent against the dollar to $1.5493, and was down one euro cent against the euro at €1.4210.
However, the FTSE 100 recouped some early losses to stand 5.68 points lower at 6,746.73.
Analysts had been expecting two of the Bank's monetary policy committee members to vote for a rate rise, with some even suggesting three could back an increase.
But in the end, only Ian McCafferty voted in favour of lifting rates from the historic low of 0.5%.
"The chances of an interest rate hike before the end of 2015 have seemingly receded markedly; indeed, it looks more questionable as to whether the Bank of England will act early on in 2016," said Howard Archer, chief UK and European economist at IHS Global Insight.
On the stock market, shares in RSA Insurance fell 1.7% after Zurich Insurance said it would not overpay for the UK company. Zurich admitted last month it was considering making a bid for RSA.
Shares in mining firm Rio Tinto edged up 0.2% despite the company reporting a sharp drop in second-quarter profits, as the sector continues to be hit by falling commodity prices.
Underlying earnings fell 43% to $2.9bn, with earnings at Rio's iron ore division down 55% to $2.1bn.
Shares in insurer Aviva rose 1.3% after it reported half-year operating profits of £1.17bn, up from £1.07bn last year and ahead of analysts' expectations.
