This is the claim of English Apples & Pears chairman Adrian Barlow, who said that fresh sales of the cooking variety have been 15 per cent higher than last season.
He added that, up to 1 March, some 58 per cent of this season's Bramley crop has been sold, compared to 45 per cent last season.
"The performance of Bramley has been very strong," Barlow said. "The fact that we sold 58 per cent reinforces the idea that there's likely to be a shortage for fresh stock at the end of June/beginning of July for this season. I think there's going to be a shortfall."
He said the shortfall was actually a good sign of the variety's rising popularity - which he attributes to good planting and promotional activity in October aimed at increasing the impact of Bramley in stores.
He added that the multiples have also been devoting more shelf space to Bramley. "They've introduced new packs so it's easier for consumers to find the products."
High crop yields of dessert apples such as Gala, Braeburn and Egremont Russet - and an increased desire by consumers to buy more UK-grown fruit - has led to an increase in the amount of Class One produce sold to supermarkets.
Barlow said: "We have sold 18 per cent more dessert apples this year than last year, with record crops for Gala and Braeburn. That means the multiples have had to sell 18 per cent more than they did a year ago just to stand still in terms of market share."
He added that he was very optimistic about the future of English Apples & Pears - which currently supplies some 35 per cent of the UK market. "We are probably looking at increasing our sales so that we supply 50 per cent over the next few years," he said.
However, he warned growers and marketers that "planned partnership productions" would be necessary to ensure that "production levels match demand for the variety".
"Owing to the large size of this year's Cox crops, for example, it's been necessary to promote the variety for longer than desirable - so we need to remember to reduce our production levels to suit the amount we need to sell."