In the year to June, the overall household costs index was up 2.5%, data from the Office for National Statistics (ONS) has revealed.
Those with mortgages faced inflation of 3.7%, compared to outright owners at 1.3%.
In addition, private renters saw overall price rises of 3.2%.
Sarah Coles, head of personal finance, Hargreaves Lansdown, said: “Stubborn mortgage rates and runaway rents are clobbering working families.
“Lurking underneath the headline figures of easing inflation is mortgage misery and ruinous rent hikes that mean some households face inflation rates as high as 3.7%.
“The overall figure looks increasingly positive, with the household costs index rising just 2.5% in the past 12 months. It’s a significant easing from 4.5% in March, and a world away from 9.8% a year earlier.”
Coles added: “The impact of higher mortgage rates is feeding through into people’s pockets, as more of them remortgage. The picture is bleak.
“Those with mortgages face a far higher inflation rate than those without.
“And those with bigger mortgages are suffering even more horrible jumps in monthly payments, which is why higher earners and parents face horrible price inflation.”