Way back in 1927, under the sweltering heat of the Texas sun, the Southland Ice Company was quietly making a fortune carving blocks of ice from ‘ice-docks’ so people could keep their food fresh at home. And then, disaster struck.

General Electric released its Monitor-Top refrigerator on to the market. It quickly sold a million units. Other fridges followed. And in a sleepy corner of Dallas, ice-dock manager ‘Uncle Johnny’ Green watched his profits melt away.

Then came his eureka moment. Wouldn’t it be convenient for his remaining customers if they could pick up grocery essentials, like bread, milk and eggs, after the grocery stores had closed for the day, and on Sundays, when they never opened at all?

His hunch paid off. Quickly back in the black, Green added soap, baking flour and canned goods to his shelves. Word spread. And the big boss swung by to take a look at what was going on.

Joe C Thompson Jr, later president and chairman of Southland, liked what he saw. He took Green’s idea and ran with it, opening more stores. However, rather than build them on the street, Thompson ordered they be built 60ft back, so motorists could conveniently pull in and out. He also started trialling selling petrol.

By the 1930s, all of Thompson’s ice/grocery stores, which he christened Tote’m stores, now opened from 7am to 7pm, seven days a week. The chain continued to thrive. Then, in 1939, Hitler invaded Poland.

The outbreak of WW2 was a pivotal moment for convenience. The vast majority of Southland’s ice was bought by the government to use for rail shipment of perishables, so Thompson turned his attentions to grocery, adding frozen foods, fresh produce and soft drinks. By 1946, with sales soaring, Thompson introduced new opening hours of 7am to 11pm seven days a week. And he changed the name to 7-Eleven.

In the 1950s and 1960s, US citizens spilled out from congested cities in search of space and fresh air, and sales accelerated. In the 1970s 7-Eleven expanded globally, opening stores in Mexico, Japan and the UK. Group sales hit £2bn. The 1980s and 1990s saw more expansion and store numbers hit 20,000 by the millennium.

As global retail success stories go, then, 7-Eleven ranks right up there. However, the UK doesn’t feature on the roll of honour. After launching in 1971, the estate grew to 55 stores, but it struggled to gain traction, and in 1997 Budgens bought the chain for £5.8m, and the 7-Eleven fascia disappeared from UK high streets. But for how long?

At the end of March this year, VP and head of international Chris Tanco said he was looking at the UK as it bids to expand 7-Eleven to 80,000 stores by 2020. He added that after carrying out a “post mortem” on its performance the first time around, he hoped the company would be back “before the market takes off economically.”

So what are its chances, and how would it go about making a comeback? They may already be “a little bit late to the party,” says head of retail at Christie & Co, Steve Rodell. “It’s a very crowded marketplace, but, if they do want to, the most cost effective way would be to take out one large company. And there are certainly a few targets they can aim for.”

Rodell speculates there are “obvious starting points. Let’s assume they go down the same franchise route they have around the world. They would need someone like Budgens/Londis or Costcutter, buy the whole shooting match, and make a big entrance.”

However, a smash and grab raid is not without challenges. “They would have to contend with the major multiples and consider the logistics. That’s before you start getting into location issues, which are tricky for everyone. Plus, if a group of stores came up, domestic companies would always be interested. Asda has stated its intentions. And I keep hearing rumours that Morrisons has approached Musgrave about Budgens. Based on what we hear, I would speculate that Musgrave is just trying to line up the ducks internally.”

If 7-Eleven does want to start a new chapter in the UK (and some industry insiders are certain it will), it clearly has the funds to do so. Yet this week, despite Tanco’s comments, a spokeswoman insisted the company had “no immediate plans to return” to the UK - showing that for now, at least, 7-Eleven is content to play it as ice-cool as one of the Slurpees on which its fortune, and its reputation, were built.