By joining forces Countryside and Vistry would have a combined market value of about £2.75 billion, equivalent to $3.2 billion, based on their latest values. The combined entity would gain greater scale to better combat the risk of a slowing housing market in the U.K. amid record-setting inflation, rising interest rates and the prospect of a lengthy recession.

Last year, Countryside built 5,385 homes across parts of Britain, while its bigger rival delivered 8,639 units, according to the companies’ annual reports.

The stocks of both Countryside and Vistry are lower so far this year. Countryside, though, has underperformed and the company has suffered from senior management upheaval, placing it under greater shareholder pressure to strike a deal.

In January, the company’s then chief executive resigned following the release of disappointing profit and revenue results. That same month, Peter Lee, a partner at Browning West, which currently owns about 15% of Countryside, joined the board.

Then in June, the builder, which has most recently been headed by interim co-chief executives, put itself up for sale. That move came following pressure from Browning, which focuses its investments in North America and Western Europe, and Countryside’s rejection as too low of a £1.5 billion takeover offer from Inclusive Capital Partners LP.

Inclusive is a San Francisco-based hedge-fund manager. Its founders include

Jeffrey Ubben,

who previously founded ValueAct Capital.

Inclusive Capital had previously indicated that it supported the auction process and would participate. It owned about 9% of Countryside shares as of May 27, according to a regulatory filing. Its current position couldn’t be learned.

A combination of economic uncertainty and the fallout from Russia’s invasion of Ukraine has made deal making particularly hard because of the challenges of valuing a target company. A deal involving mostly stock, like the transaction that Countryside and Vistry are targeting, can overcome that challenge by allowing shareholders of each company to hold shares in the combined entity and benefit from cost savings and any stock gains if the merger succeeds and overall market conditions improve.

Britain’s Sunday Telegraph newspaper earlier reported Vistry was exploring a takeover of Countryside.

Write to Ben Dummett at ben.dummett@wsj.com