The new vegan sausage roll launched by Greggs is “flying off the shelves”, leaving Britain’s biggest bakery chain unable to keep up with demand after selling hundreds of thousands in the first week.

The £1 rolls have been selling out rapidly, depleting the stocks held at Greggs’ factory in Newcastle, where they are made and frozen before being sent out to shops to bake.

Roger Whiteside, the chief executive, said the firm had been taken by surprise over their popularity and the level of publicity surrounding the launch, and was ramping up production in response.

“Now that we know it is selling, we want to get it out there as quickly as possible. The shops that do have it are selling out instantly and the shops that didn’t get it are screaming for it.”

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The Quorn-filled vegan alternative to the traditional meat version was launched in 950 of Greggs’ 1,950 shops on 3 January, coinciding with the beginning of Veganuary, a growing movement that encourages people to embrace plant-based diets during January.

“It’s literally flying off the shelves,” said Whiteside, who added it was the fastest-selling new line in the six years he had been with the company. He said the popularity of the new vegan roll had not dented sales of Greggs’ traditional sausage rolls, which also increased last week. Greggs sells about 1.5m of the meat version every week.

Whiteside made the comments alongside a trading update for the final three months of the year. The company said it had enjoyed a strong finish to 2018, prompting it to raise its profit guidance for the second time in two months, bucking the trend among high street retailers.

Shares jumped nearly 7% to a record high of £14.61 after Greggs said December had beaten expectations, thanks to bumper sales of its festive bake and mince pies as well as its hot drinks and breakfast range.

The company is expecting pre-tax profits of at least £88m for 2018, having already upgraded its guidance in November, when it said profits would be at least £86m. Greggs made a pre-tax profit of £81.8m in 2017.

Greggs has increased sales and profits despite a tough backdrop for high-street retailers struggling with rising business costs, a switch to online spending and faltering consumer confidence as Brexit looms.

Whiteside said that sales at its high-street shops were still growing – albeit at a slower rate than its stores at other locations such as railway stations, retail parks and service stations – helped by strong demand for its breakfast ranges as well as its traditional steak bakes and sausage rolls.

“I think it demonstrates how our business has changed,” he said. “Our high-street shops are less reliant on shopping missions and that’s making us more resilient. People working on the high street are coming in for breakfast before the shops are open.”

Total sales rose 7.2% in the year to 29 December, while like-for-like sales – stripping out the impact of sales in shops open for less than a year – increased by 2.9%. In the fourth quarter alone, like-for-like sales were up 5.2%.

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Greggs has prided itself on making changes to the products on offer to suit changing consumer tastes, including a greater focus on the “food-on-the-go market” as well as the traditional bakery lines.

Whiteside said: “In the year ahead we will continue to innovate with products designed to reflect changing consumer tastes and by opening in new locations that make Greggs even more accessible to customers.”

The bakery chain opened 149 shops in 2018 and closed 50. Whiteside said the number of Greggs stores would pass the 2,000 mark this year and the plan thereafter was to open about 100 shops a year until it reaches 2,500.