CPIH inflation, The ONS' headline measure which includes owner occupiers’ housing costs, was also 1.5% in October, down from 1.7% the previous month.
The largest downward contribution came from electricity, gas and other fuels as a result of changes to the energy price cap.
Further downward contributions came from furniture, household equipment and maintenance; and recreation and culture.
Rupert Thompson, head of research at Kingswood, commented: "These numbers follow hard on the heels of the downbeat economic data released earlier in the week which showed a slowdown in underlying wage growth, a fall in employment and the weakest GDP growth since 2010.
"Altogether, this crop of data suggests any move by the Bank of England over coming months is more likely to be a rate cut than a hike. Even so, the most likely outcome remains that the Bank remains on hold – particularly now there are signs the worst of the global economic slowdown is behind us.”