Bank of England policymakers voted unanimously to keep interest rates on hold earlier this month but there were signs that more of them were edging closer to pushing for a first hike since before the financial crisis.
Minutes of the Monetary Policy Committee's meeting, which ended on July 8, showed its members voted 9-0 to leave rates at their record low of 0.5 percent.
"For all MPC members, the policy decision this month was clear cut," according to the minutes which were published on Wednesday.
However, for "a number" of policymakers, the risks of inflation rising above the Bank's 2 percent target was rising and it was the "very material factor" of Greece's debt stand-off that influenced their vote to keep rates on hold.
"Absent that uncertainty, the decision between holding Bank rate at its current level versus a small increase was becoming more finely balanced," the minutes said.
At its previous meeting, in June, the BoE said that for two policymakers, the decision rates was already finely balanced.
The July minutes showed that for most members, keeping rates on hold would still have been appropriate even without the problems in Greece and the volatility in China's financial markets.
The vote by the MPC also took place on the day that British finance minister George Osborne announced his post-election tax and spending plans.
The BoE said the committee had been briefed by the finance ministry that the new budget plans were unlikely to result in more of a drag on growth than the Bank had previously assumed.
All 17 economists who took part in a Reuters poll had predicted that the MPC would remain united in voting for no change in rates in July.