The policymakers agreed that the recovery was looking more assured, though there were some tentative signs of a slight slowdown that had been forecast for the second half of the year.
The ongoing weakness of wage growth was becoming more striking - especially against a backdrop of strong employment growth - making it hard to judge the degree of slack in the labour market.
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Some policymakers saw this as a reason to focus on the rapid pace at which slack was being used up, and that this was a reason to consider raising rates sooner rather than later - in part to assess the economy's response to a small rate rise.
Others thought this could be dangerous at a time when there were signs of weakness in the global economy and British wages were lagging behind inflation, and that an unexpected rate rise could have an outsize impact on the recovery.
Policymakers said they would discuss labour developments more in August, when the BoE will prepare its quarterly economic forecast update.
BoE Governor Mark Carney said last week that he did not know exactly when interest rates would start to rise for the first time since 2007, as it would depend on the strength of economic data, but reiterated that the pace of rate rises would gradual.
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This view was shared more widely in the minutes.
Many people in the financial markets expect interest rates to rise before the end of the year, and a majority of economists polled by Reuters forecast a rate rise before March.
Britain's economy is growing rapidly and figures due later this week are expected to show quarterly growth of 0.8 percent in the second quarter of this year, taking gross domestic product above its 2008 pre-crisis peak for the first time.
But price pressures remain muted, despite a spike in inflation to 1.9 percent in June.
Wage growth excluding bonuses - which the BoE views as an important guide to the amount of slack in the labour market - slowed to a record low 0.7 percent in the three months to May.