The data found that demand induced by the second wave of lockdown will keep price growth in positive territory at 3.5% in 2022, 3.0% in 2023 and 2.5% in 2024.
London is set to underperform the rest of the country until the house price cycle ends in 2024.
Hamptons forecast prices in the capital to end the year up 1.5% and then rise by 1.0% in 2022, 1.5% in 2023, before accelerating to 3.0% in 2024.
The North East was expected to be the top performer over the next four years.
Hamptons said house prices will rise 21.5% in Q4 2024, outpacing the Great Britain average of 13.5%.
A record-breaking first half of the year has meant that more homes will have sold in 2021 than in any year since 2007.
Hamptons forecast 1.5 million completions in Great Britain in 2021.
COVID-19 induced changes mean households will make more moves than pre-pandemic times.
The estate agents forecast transactions to fall marginally to 1.25 million in 2022 before reaching a new normal of 1.3 million in 2023 and 2024.
The rapid pace of rental growth will slow, as a result of which Hamptons said rents in Great Britain will likely end the year up 3.0%, before slowing to 2.5% in 2022 as affordability bites.
By the end of 2024, the estate agent expected rents to have risen by 10.0%, led by Southern regions.
Meanwhile, London will lag until growth accelerates in 2024.
Aneisha Beveridge, head of research at Hamptons, said: “The housing market has confounded expectations and forecasts in past months.
“Back in the autumn of 2020, such were the economic challenges being faced that we could not have envisaged the extraordinary demand for relocation which we have seen this year.
“But there has been a huge attitudinal change towards property, which cannot be attributed to the stamp duty holiday alone.
“People now place a higher value on their homes, having have spent more time in them than ever before.
“Flexible and remote working, which look set to continue, have encouraged households to make bigger moves.
“As a result, more homes are likely to have been sold in 2021 than in any year since 2007.
“This is why we also think housing activity will surpass pre-pandemic times in 2022 and beyond.
“The pandemic has accelerated the closing of the house price gap between London and the rest of the country.
“Even so, we still expect London to underperform the rest of the country until 2024, when the cycle is likely to end.
“While we will see a degree of levelling up over the next few years, the gap between house prices in the capital and the other regions is likely to be wider than that seen at the end of the previous cycle in 2007. And this divergence will set the pattern for future performance.”
