The minutes also highlight policy-makers' awareness of the dangers of a build-up of financial imbalances, notably in the housing market, if rates are, in line with MPC guidance, raised only gradually and to levels well below the average before the economic crisis.
Although the MPC's nine members were unanimous again this month in voting to hold base rates at a record low of 0.5 per cent, where they have been since March 2009, the minutes of the May 7 and 8 meeting reveal a "variety of views" among members on the appropriate path of monetary policy.
Signalling some members are moving closer to voting to raise rates, the minutes state: "The committee would continue to refine its views as the economy evolved, and for some members the monetary policy decision was becoming more balanced."
Howard Archer, chief UK economist at consultancy IHS Global Insight, said: "The outlook for monetary policy is starting to look a lot more uncertain, with the minutes ... indicating that opinions within the committee are diverging on about exactly when monetary policy should start to be gradually tightened. There are clear indications in the May minutes that some of the more hawkish MPC members are starting to get twitchy."
He added: "We retain the view that interest rates are most likely to start edging up in the second quarter of 2015, but there is clearly a very real and growing likelihood that the Bank of England will act before then."
The minutes also signal MPC members are wary about the impact on the economy of a rise in base rates, and they chime with the view signalled in recent days by Bank of England Governor Mark Carney that monetary policy would not be the appropriate tool to cool the housing market, if such action were required.
They highlight the Financial Policy Committee's role in dealing with issues relating to financial stability.
Detailing MPC members' discussions two weeks ago, the minutes state: "The committee's February guidance embodied the expectation that, when Bank Rate began to rise, it would do so only gradually and to a level materially below its pre-crisis average.
"Although such a path for policy ran a greater risk of a build-up in financial imbalances, particularly in the housing market, the committee noted that the mitigation of such risks was, in the first instance, the responsibility of the FPC: monetary policy should be only a last line of defence."
While setting out the case for moving gradually, the minutes also signal a view among some members that such an approach might mean the first rise in rates should come earlier.
Setting out this debate, the minutes state: "The case for moving gradually and cautiously was reinforced by uncertainty over the likely impact on the economy of a rise in Bank Rate. It could be argued that the more gradual the intended rise in Bank Rate, the earlier it might be necessary to start tightening policy. Against that, if productive potential were in part related to the level of demand, then the earlier policy was tightened the greater the risk of incurring a substantial cost in foregone output.
"Committee members placed different weights on these considerations."