Limited evidence that the British economy was generating too much inflation pressure meant the BoE could afford to hold off on rates, rather than relying too heavily on theories about how growth, inflation and wages are linked, he said.
The BoE's Monetary Policy Committee voted 7-2 to raise rates for the first time in more than a decade on Nov. 2. Governor Mark Carney has justified the decision by pointing to low levels of unemployment that were likely to trigger faster wage growth.
Carney also mentioned low productivity growth had increased the risk that Britain's sluggish economy, weighed down by uncertainty about Brexit, could generate persistent inflation.
But Cunliffe said past BoE forecasts of higher wage growth had proven wrong, and the central bank had time to wait to see if this time was different.
"The low level of domestic pressure on inflation now ... (makes) it possible to wait before tightening policy until there is clear evidence that pay growth is responding to the level of unemployment in line with our forecast," he said in a speech to economics students at the University of Oxford.
Figures earlier on Tuesday showed that British inflation held at a five-year high of 3.0 percent last month, undershooting BoE forecasts that it would peak at 3.2 percent before falling slowly back towards its 2 percent target.
Wage growth remains weak by pre-crisis standards in Britain and other countries around the world.
Data due on Wednesday is expected to show the pay of British workers increased by just above 2 percent on a year-on-year basis in the three months to September, according to a Reuters poll of economists.
Many economists share Cunliffe's view that there was little need to raise rates by a quarter percentage point to 0.5 percent earlier this month, especially given the uncertain economic outlook caused by the Brexit process.
Most do not expect the BoE to raise rates again until 2019.
Uncertainty was a common problem for central bankers, but the current situation was trickier than usual, Cunliffe said.
Aside from the difficulty of predicting the reactions of households and businesses to the ongoing Brexit talks, the link between low unemployment and faster wage growth appeared to have weakened in Britain and other countries, he said.
"Given the ... serial disappointments we have had in recent years in forecasting the impact of unemployment on pay growth, there is ... a not immaterial risk that ... domestic inflation pressure will undershoot the (Monetary Policy) Committee's collective expectation," Cunliffe said.
Even if this "longish leave of absence" in historic economic relationships turned out to be temporary, central bankers needed to be cautious, he added.
"Against that background ... I tend to put more weight on the evidence we can or cannot see in the data and a little less on the unobservables and on how we think the economy works," Cunliffe said.
(This version of the story has been refiled to clarify which policymaker referred to in paragraph 4)
(Reporting by David Milliken; Editing by William Schomberg)
By David Milliken