McCafferty was one of three members of the Bank’s Monetary Policy Committee (MPC) who voted to raise the base rate in June.
However, he is to be replaced on the nine-member rate-setting committee at the end of August and has used his final public speech before stepping down to urge action by the MPC.
The economy outlook calls for around three rate increase over the course of the next three years, McCafferty said.
He added: “That outlook, combined with the risks around it, also suggests that we should not dally in making the next move.
There is a significant chance that inflation will remain above 2% in two years, thanks to higher wages and rising energy prices, the policymaker suggested.
He added: “As a result, continuing with the slow reduction in monetary stimulus without undue delay could well prevent the need for a more aggressive tightening later on.”
Economic data over the coming weeks will be closely scrutinised by markets for clues over whether more members of the MPC will vote for a rate rise in August.
Ruth Gregory, senior UK economist at Capital Economics, said: “It’s unlikely to take much to sway the wavering MPC members to vote for an August rate hike.
“A solid set of Markit/CIPS surveys for June and some improvement in the upcoming industrial production and construction figures should be enough to tip the balance in favour of the hawks.
“Overall, we continue to expect rates to rise in August and again in November.”