The FTSE 250 group raised its forecasts for house price inflation this year to 4% from zero following the measures unveiled by the Chancellor in the Budget.
Savills said it has been surprised by the strength of the bounce back in the market after the first Covid-19 lockdown in March, but now sees strong growth across the country until 2025.
London is expected to see rises on average of around 13% during this period, but cities in the north-west and Yorkshire are set for rises of up to 30%, the agent believes.
Lucian Cook, head of residential research at Savills said: “The outlook has improved since the beginning of the year given the speed of the vaccination programme, the expected relaxation of social distancing measures and government support for both jobs and the housing market.”
A home costs an average of £221,000 in Yorkshire and Humberside and around £228,000 in the north-west compared to £548,000 in the capital.
In the Budget, Rishi Sunak extended the current stamp duty holiday for sales under £500,000 while also bringing in a new mortgage guarantee scheme to help first-time buyers.
Cook said that the likelihood that interest rates would stay much lower than expected before the Covid-19 pandemic would underpin demand for the next few years.
Shares in Savills rose 1% higher to 1,079p, while housebuilders were mixed, with Barratt (LON:BDEV) and Berkeley (LON:BKG) more than 1% higher, Taylor Wimpey (LON:TW.) flat but Bellway (LON:BWY) and Redrow (LON:RDW) around 2% lower.