The site recorded more than six million daily visits on 5 and 6 January.
Rightmove has recorded its busiest ever start to a new year, with site visits up 30% year-on-year.
The site recorded more than six million daily visits on 5 and 6 January.
In addition, the number of people contacting estate agents about properties to buy was 11% higher than at the start of 2020, and those enquiring about a property to rent was up by 22%.
The record number of site visits came following Prime Minister Boris Johnson's announcement of a third national lockdown.
Rightmove has attributed the rise in prospective buyers to the impending conclusion to the stamp duty holiday.
Tim Bannister, director of property data at Rightmove, said: “January is usually one of our busiest months of the year as people start to make new year plans to move.
“As was the case at the start of last year when we also had the post-election bounce that gave hope of an active spring market, before that all changed with the temporary closure from March until May.
“We didn’t know how this year would start with so much change and uncertainty around restrictions, but it’s been reassuring for those people hoping or needing to move that the demand we’ve seen so far is the highest we’ve ever had in January.
“The housing market has been allowed to stay open during these latest lockdowns and agents have already spent months working in a COVID-secure way and creating a number of property videos.
“[As a result] buyers and renters starting out on their search this year will find that, alongside the safe viewing protocols, more agents are offering virtual viewings to help buyers and renters better shortlist the properties they want to go and see.”