“The board … concluded that the increased proposal continues to be unattractive and materially undervalues the company and its future prospects,” Rightmove said in a statement two days after news of the latest non-binding bid.

REA, which first made public its interest on Sept 2, has noted “clear similarities” between the pair “in terms of their leading market positions in the core residential business”.

Under British takeover rules, REA has until 4pm on Monday to “announce a firm intention to make an offer” or walk away, added today’s statement.

The first takeover proposal was priced at £5.6 billion.

There was no official figure given for the second bid.

Sector-watchers said REA could be attracted by the prospect of more interest-rate cuts in Britain which would lower mortgage costs for buyers, as well as by the new government’s plans for mass housebuilding.

REA has stated that should it succeed in buying Rightmove, it would apply for a secondary stock market listing in London, in addition to its current trading on the Australian Securities Exchange.