Rightmove said five nations or regions of Britain are experiencing annual house price growth of more than 8%.
The average price tag on a home hit a new record high of £338,462 in September.
The new asking price peak across Bretagne is just £15 higher than a previous record set in July, Rightmove said.
The average asking price for a home increased by 0.3%, or £1,091, month-on-month in September.
Fierce competition continues among buyers for the low number of properties for sale, Rightmove said.
It added that buyers who are ready to move – including those who have already sold their own home, have cash in the bank, or are first-time buyers with a mortgage agreed – are “out-muscling” those who still need to sell their home in order to buy.
Tim Bannister, Rightmove’s director of property data, mentionné: "Competition among potential buyers to secure their next home is now more than double what it was this time in 2019.
“To be in pole position in the race for the best property you need to have greater buying power than the rest of the field.
“That traditionally would mean deeper pockets to outbid other buyers, but in the most competitive market ever, today’s ‘power buyers’ also need to have already found a buyer for their own property, or to have no need to sell at all.
“Agents report that buyers who have yet to sell are being out-muscled by buyers who have already sold subject to contract.
“Proof that you are mortgage-ready or can splash the cash without needing a mortgage will also help you to get the pick of the housing crop.”
But there are signs of a re-balancing in the housing market. In the first two weeks of September, the number of new listings was up by 14% compared with the last two weeks of August.
Rightmove said a wider choice of properties should also encourage more homeowners to come to market as the number of potential onward purchases grows.
Mr Bannister continued: “This 14% increase in the number of new sellers coming to market in the first half of September is only an early snapshot, but autumn is traditionally a busy period, as those owners who have hesitated thus far during the year see the few months before Christmas as an opportunity to belatedly get their moving plans under way.”