"For now, the Bank is not seeing enough to abandon its wait-and-see approach," said Schroders senior economist George Brown.
"Despite the sharp rise in energy prices, the majority appear unconvinced this will translate into more persistent domestic inflation."
In updated forecasts, the BoE's central projection showed inflation rising to 3.2% later this year from a 15-month low of 2.6% in June.
That is a softer inflation outlook than in the Bank's last full forecasts in April, but similar to what it predicted in June.
Central bankers’ jobs have been complicated by the stop-start U.S.-Iran war which has flared up again in recent weeks, pushing oil prices higher.
Brent crude oil prices LCOc1 have risen more than 20% this month, although at around $90 a barrel they remain well below late April’s peak of $126 a barrel.
The BoE's Bailey and other policymakers stressed that there are few signs the rise in oil prices this year are broadening to push up inflation in non-energy sectors.
The MPC in its statement said there were "clear signs" that inflationary pressures were abating in the domestic economy, citing a weakening labour market.
"The overall decision leans dovish," said ING developed markets economist James Smith.
"Officials are visibly more confident that we won’t see the sort of second-round effects they feared at the start of the Middle East conflict."
Britain's FTSE 100 .FTSE extended gains slightly and was last up 0.4% at a fresh record high on Thursday.