Sterling dropped 0.5% against the dollar to trade at $1.2872, while it also shed a similar amount against the euro to 1.1844 euros.
The Bank trimmed its 2017 growth forecast and said household spending was slowing more quickly than expected.
Rates were held at 0.25%, as expected, after a 7-1 vote by policymakers.
Some analysts had speculated that a second member of the Bank's Monetary Policy Committee might vote in favour of a rate rise.
On the stock market, the FTSE 100 index closed almost flat, up 1.4 points at 7,386.6, helped by a positive performance from mining shares.
Silver miner Fresnillo rose 5%, while Randgold Resources and Antofagasta also rallied.
Pharmaceuticals firm Hikma dropped 8.2%, making it the biggest faller, after US regulators delayed approval for a new drug.
Hikma has been developing a generic version of GlaxoSmithKline's lung drug Advair, but US regulators found "major" issues with its application.
The company said there was now "a low likelihood" that the drug would be approved this year.
Centrica, the British Gas owner, fell a further 5.4% after it went ex-dividend and JP Morgan cut its rating to "underweight" from "overweight".
The bank's analysts pointed to concerns around the impact of regulation given millions of British Gas customers are on standard variable tariffs, and the potential threat of a price war.
BT fell 4.5% after reporting a slide in annual profits.
Mondi was another faller, down 1.7% after the South African packaging company reported lower profits.
First-quarter operating profits dropped 6% to 252m euros (Â£212m) as a result of lower selling prices and rising costs.
The pound fell sharply after the Bank of England's latest Inflation Report was seen as ruling out any rate rises for some time.