Sheffield's house prices have increased by 0.8% per month in the three months to January, Liverpool's prices have risen by 0.7% per month and Glasgow's have risen by 0.6% per month.
Cardiff's prices have also increased by 0.8% each month and London prices have risen by a steady 0.5% per month in the last three months.
Overall house price growth stands at 7.9% annually to January 2015.
Richard Donnell, director of research at residential analysts Hometrack, said: "House price growth within cities reflects the strength of their local economies and the demand for housing.
"House prices continue to rise off a low base as pent-up demand returns to the market supported by record low mortgage rates, an improving economic outlook and rising earnings.
"Existing homeowners remain reluctant to put their homes on the market, creating scarcity and keeping an upward pressure on prices."
Areas which performed strongly in 2014 are cooling, as on an annual basis London prices are up 13.6%, Bristol's have increased by 10.8% and Oxford prices have risen by 8.6%.
Donnell added: "The outlook for 2015 is a balance between the scale of the affordability driven slowdown in the high value, high growth markets and the continued recovery in lower value markets."
