At least one member of the Monetary Policy Committee said signs that the economy was accelerating meant it would have been "preferable" to have left them on hold.
The MPC decided unanimously to hold rates at 5 per cent two weeks ago, saying a hike would send the wrong signal to the financial markets about the future path for interest rates.
The decision, combined with higher than expected retail sales - especially of household goods - fanned speculation that rates have troughed and that the next move will be up.
The pound rose sharply against the dollar. It hit a peak of $1.5756, up from pounds 1.5686, before easing off to close at $1.5738. The minutes revealed the MPC discussed whether June's 0.25 per cent cut was a mistake.
"Developments over the month have probably strengthened that argument," the minutes said. "Indicators such as domestic demand, money data and housing market activity were pointing to a less benign inflation outlook further ahead."
Mervyn King, the deputy governor of the Bank of England, voted against June's rate cut, which was backed by the other eight - a move seen as a surprise at the time.
The MPC decided not to reverse the cut as it would affect business and consumer confidence "disproportionately" and would give the "wrong signals" on future monetary policy.
David Smith, chief economist at stockbroker Williams de Broe, said: "I think the last cut, with hindsight, looked shaky at the time and now looks like a mistake.
"If the figures carry on in this vein, especially with the housing market overheating, we could see a quarter-point hike in interest rates."
The minutes said that activity strengthened in June, while money and employment data suggested growth in the second quarter would be stronger than expected when it cut rates.
"On balance, the committee agreed that the news over the past month suggested the projected recovery in activity seemed to be underway and was, if anything, a little faster than expected," the minutes said.
The MPC was worried that private sector earnings were falling and that the pound had fallen against the dollar but said it wanted to wait another month for the August inflation report.
The minutes said the committee believed underlying inflation would remain below its 2.5 per cent target in the short term but that the "extent and duration of any undershoot was uncertain".
Retail sales rose 3.8 per cent in the year to June, the highest since May 1998, and ahead of forecasts of 3.3 per cent.
The Office for National Statistics said the data confirmed that the underlying rate of growth had picked up since the turn of the year. But it added: "They do not necessarily point to a pick up and we need more evidence."
Household goods sales in the three months to June were up 7.1 per cent on a year ago. Electrical goods, which includes big ticket items such as fridges and TVs, rose by 17 per cent.Reuse content