The average price tag on a home in Britain hit a new record high of £323,530 in October, according to a property website.
Asking prices were 1.1%, or £3,534 in cash terms, higher than in September, Rightmove said.
Prices are now 5.5% or £16,818 higher than a year ago, marking the biggest rate of increase for more than four years, it added.
Despite the economic crisis caused by Covid-19, with the associated job losses and mortgage lenders having pulled many low deposit loans, Rightmove predicted the annual rate of price growth could peak at around 7% before the end of this year.
A temporary stamp duty cut introduced in July has given buyers a window of opportunity to save money on their moving costs.
But some sellers may be getting too optimistic about what people will pay, the report said.
Tim Bannister, Rightmove’s director of property data, said: “Previous records are tumbling in this extraordinary market, and there are still some legs left in the upwards march of property prices.
“We predict that the annual rate of growth will peak by December at around 7% higher than a year ago.
“Many buyers seem willing to pay record prices for properties that fit their changed post-lockdown needs, though agents are commenting that some owners’ price expectations are now getting too optimistic, and not all properties fit the ‘must have’ template that buyers are now seeking.
“Not only is the time left to sell and legally complete before the March 31 stamp duty deadline being eaten away by the calendar, but more time is also needed because the sheer volume of sales is making it take longer for sales that have been agreed to complete the process.
“Sellers and their agents should therefore be wary of being too optimistic on their initial asking price, as whilst activity levels continue to amaze, there are some signs of momentum easing off from these unprecedented levels.”
Rightmove said that despite the effective market closure between late March and mid-May, 2% more sales have been agreed so far this year than in the same period in 2019.
This indicates that the recent jump in activity is not just down to demand from earlier in the year having been put on hold.
Demand is still outweighing supply, particularly for quality properties marketed at the right priceMartin Robinson, Hunters
As well as the new price record, Rightmove said the average time to sell a property is also at a new record of 50 days. This is 12 days faster than a year ago.
The number of active buyers contacting estate agents in September was 66% up on a year earlier, only marginally down on a peak of 67% higher in July.
Rightmove also recorded a 49% increase in traffic in September compared with the same period last year, which is the biggest year-on-year jump since 2006.
Mr Bannister continued: “With the number of buyers contacting agents still up by two-thirds on a year ago, there is plenty of fuel left in the tank to drive further activity in the run-up to Christmas and into next year.
“There have also been Government promises of additional low-deposit mortgage support for first-time buyers, which could prove to be timely as we run up to March 31.
“It appears that the current momentum, assisted by the prospect of stamp duty savings, is helping to keep the housing market healthy.
“Estate agents have worked hard to give confidence to sellers and buyers alike that property viewings can be conducted safely, and early signs show that market activity still remains high in areas with stricter local lockdowns.”
Martin Robinson, director of Hunters, said: “Demand is still outweighing supply, particularly for quality properties marketed at the right price, and we’re regularly experiencing sales going to best and final offers…
“We’re also seeing changes in the habits of the consumer, with many saying that there is no need to be on the doorstep of their workplace and are looking to move to a more rural or affordable location, broadband speed permitting, to work remotely where they can get more for their money.”
Dominic Agace, chief executive of Winkworth estate agents, said: “We are now seeing sellers join the property market, catching up with buyers’ early start.
“With both tracking well ahead of 2019 levels, we expect this activity to continue for the rest of the year.
“However, with increasing supply and uncertainty around Covid, we expect prices to flatten out now we are past the peak autumnal market.”