The BoE raised interest rates from crisis-era lows on Thursday but that failed to boost the pound as the central bank also signalled it was in no rush to tighten policy further.
Raising questions over Thursday's hike, the closely-watched IHS Markit/CIPS UK Services Purchasing Managers' Index (PMI) on Friday came in softer than all forecasts in a Reuters poll, with weaker-than-expected growth in Britain's huge services sector in July. The pound was largely unmoved, however.
With less than eight months to go until Britain leaves the European Union, the government has begun talking more publicly about the prospect of leaving without a formal agreement on its future relationship with the bloc.
The pound dropped 0.3 percent to an 11-day low of $1.2975 , close to the 10-month low of $1.2958, before recovering as the dollar weakened. The pound's travails have coincided with a broad rally in the dollar this week.
Against the euro, sterling traded flat at 88.97 pence per euro.
"I don't think the case for hiking rates is very strong. The UK growth story is relatively weak," said Tim Graf, State Street Global Markets' EMEA Head of Macro Strategy. "I am still biased for some downside."
Britain's economy has recovered from a weather-induced slowdown in the first quarter but sentiment is fragile.
Inflation remains above the BoE's target of 2 percent but domestic sources of price rises are limited so far and have yet to feed through to significant upward pressures on wages, particularly given historically low levels of unemployment.
With the next six months set to be dominated by efforts to agree a deal on trade with the EU, money markets do not expect the BoE to hike rates again until late next year.
Carney hinted on Friday that interest rates are likely to rise to around 1.5 percent over the next three years, based on the expectations of financial markets.
"That's not a prediction, that's not a guarantee, but that's not a bad rule of thumb given the current state of the economy and the momentum in the economy," he told the BBC.
The market is pricing in one rate hike in 2019 for September, based on the money market "SONIA" curve.
"We remain more hawkish than the market (the short-end rallied modestly yesterday) and see the next 25bp (basis point) move by the Bank being in February next year," said George Buckley, UK economist at Nomura.
"Much will likely depend on how the Brexit negotiations have fared between now and then -- with the next six months crucially important in that respect."
The pound, one of the best performing currencies at the start of 2018, has lost 10 percent of its value since hitting a post-Brexit referendum high in April of $1.4377.
Sterling has held up far better against the euro, although it is still down 3.4 percent since April.