Ian McCafferty and Michael Saunders both wanted the base rate to immediately rise to 0.75%.
But the majority of the rate-setting committee voted to maintain at the current level.
The split has raised expectations that a rate rise will be pushed through at the next meeting in May.
A statement from the Bank of England today said: “As in February, the best collective judgement of the MPC remains that, given the prospect of excess demand over the forecast period, an ongoing tightening of monetary policy over the forecast period will be appropriate to return inflation sustainably to its target at a more conventional horizon.
“All members agree that any future increases in Bank Rate are likely to be at a gradual pace and to a limited extent.”
Minutes from the MPC meeting noted that wage growth is expected to rise in the coming months, while inflation will remain above target – giving further weight for the case to increase rates.
Ed Monk, associate director for personal investing at Fidelity International, said: “The message from the Bank of England to borrowers couldn’t really be clearer: get ready for higher rates now.
“Two members voted for a rate rise this month and the Bank said nothing to dispel expectations that rates will rise in May.
“Inflation has been above target for more than a year but it’s recent stronger wage growth that has prompted Mark Carney and the other MPC members to become more hawkish.
“If the Bank’s central case proves correct, the good news is that wages should be able to regain some lost ground as the currency-driven inflation that followed the Brexit result eases back and the benefits of a tight labour market at last translate into a pay-rise for workers.
“The sting in the tail will be higher costs of borrowing for indebted households.”