All nine Bank of England policymakers voted to keep interest rates on hold this month, after two of them dropped calls to raise rates from 0.5%.
Two members of the Bank's Monetary Policy Committee (MPC), Martin Weale and Ian McCafferty, had been calling for a rate rise since August.
However, January's MPC minutes showed they felt a rate rise now might cause below-target inflation to persist.
Analysts are now predicting that rates will not rise until 2016.
Last month, inflation dropped to 0.5%, its lowest rate in more than 14 years and well below the Bank's target of 2%.
As inflation is now more than one percentage point away from the Bank's target, governor Mark Carney will have to write a letter of explanation to the Chancellor, George Osborne.
The Bank has held interest rates at the record low of 0.5% for nearly six years, and analysts do not expect a change for some time.
Alastair McCaig, a market analyst for IG, said "any expectation that rates might rise in 2015 has now been quashed" and that the first or second quarters of 2016 "appear much more likely timeframes".
Mr Weale and Mr McCafferty have been voting to raise rates to 0.75% since the summer, so the unanimous vote marked "a significant shift in the expected path for interest rates" said Ben Brettell, senior economist at Hargreaves Lansdown.
"Many forecasters had been expecting the first rise to come later this year, but this now looks extremely unlikely," he said. "This further reinforces my view that they will remain on hold throughout this year and into 2016."
Lower oil prices and a supermarket price war could keep inflation below 1% for a number of months, he added.
The decision by Mr Weale and Mr McCafferty was "finely balanced" this month, the minutes said.
They believed that the sharp fall in inflation had been driven by temporary factors, but that there was still a risk low inflation may last.