Direct Line shares soared by more than 40% amid speculation rival Aviva could return with an even higher takeover offer, as a flurry of deals lit up the London market.

Aviva’s rebuffed £3.3bn approach, which was revealed on Wednesday night, was the third rejected by Direct Line this year, with the company having snubbed two previous bids by the Belgian insurer Ageas that culminated in a £3.2bn offer in March.

Despite Aviva’s insistence that the deal would bring attractive returns for both companies’ shareholders, Direct Line said the 250p-a-share bid – made up of cash and Aviva shares – was “highly opportunistic and substantially undervalued the company”.

The board said it was backing Direct Line’s executives and declined to engage further with Aviva. The move sent Direct Line’s share price climbing to more than 224p on Thursday, making it one of the biggest risers on the FTSE 250.

Aviva said a deal would create “attractive returns for both Aviva and Direct Line shareholders”.

It came as a burst of dealmaking ignited the stock market, with the cafe bar business Loungers and waste management firm Renewi becoming the latest to fall prey to takeovers.

Fortress Investment Group, the US private equity group that owns discount retailer Poundstretcher, Majestic Wine off-licence and Punch pubs group, struck a deal to buy Loungers for £338m. Operating the Lounge, Cosy Club and Brightside brands, it has 280 venues across England and Wales.

Fortress offered 310p for each Loungers share, a premium of about 30% to its closing price on Wednesday, in a deal that was backed by Loungers’ board.

The Australian asset manager Macquarie also struck a £700m deal to buy Renewi for 870p a share, a year after its lower offer for the waste firm was rejected. Renewi, formerly known as Shanks Group until a 2017 rebrand, sold its UK municipal bin-collecting business to the rival Biffa earlier this year, and is focused on Belgium, France, the Netherland and Portugal.

The diminishing number of UK-listed firms has prompted growing concern about the health of the London market. The chancellor, Rachel Reeves, promised to overhaul capital markets in her recent Mansion House speech.

“So many UK-listed companies are being taken over because the market didn’t spot the value on offer,” said Dan Coatsworth, an investment analyst at AJ Bell.

Direct Line revealed earlier this month that it proposed to cut 550 jobs as part of a turnaround plan aimed at saving £50m next year.

The Kent-based company lost almost 400,000 car insurance customers in the past year. Its chief executive, Adam Winslow, joined the company in March from its suitor Aviva, where he ran the general insurance business in the UK and Ireland.

Analysts at Jefferies said they were not surprised that Aviva’s offer was rejected, given it was a “relatively small uplift” on Ageas’s bid.

The Jefferies analysts Philip Kett and James Pearse said: “Previously, we suggested that the capital and expense synergies available to an acquirer mean that an offer of at least 270p would be more realistic.

“With this in mind, while we agree with Direct Line’s rejection of the offer, we do believe that a higher offer might be forthcoming if the board considered engaging with Aviva.”

Others suggested that Aviva, which is led by the chief executive, Amanda Blanc, could be the most appropriate owner of a company such as Direct Line.

Matt Britzman, a senior equity analyst at Hargreaves Lansdown, said: “Direct Line is playing hard to get, again … [but] there’s a case to be made that Aviva is a better suitor, given it already shares markets with Direct Line in the UK, but it’ll need to up its game – and its offer – if it wants Direct Line to take the proposal seriously.”

However, there are no guarantees of a higher offer from Aviva, and KBW insurance analysts, led by William Hawkins, said it was unlikely to go above 300p a share: “We are always cautious about the bidder’s curse, but we believe Aviva’s approach to Direct Line Group is strategically coherent, could offer considerable synergies, and is currently highly financially attractive.

“The main risk for Aviva is that it seems to be stretching an already below-average solvency ratio, so any further generosity would need to come from shares.”