The Bank of England's Monetary Policy Committee (MPC) remains unanimously against raising interest rates, according to minutes from the May meeting.
Committee members voted 9-0 in May to hold interest rates steady at 0.5%.
The minutes said that inflation was likely to remain close to zero in the very near term, reflecting drops in food, energy and other prices.
But house prices could face "upside risks" in the second half of the year.
After the minutes' release, the pound was trading close to its high for the session, at $1.55.
Two out of the nine policymakers stayed "finely balanced" between voting to hold or raise bank rates, the minutes said.
Committee members also voted unanimously in favour of not increasing the bank's £375bn asset purchase programme, known as quantitative easing.