One device was listed with a previous sale price of £2,378, but was "reduced" to £1.58.
The computer firm briefly took its UK store offline on Saturday to resolve the error, and said it would not honour the sales that had been made.
"We apologise sincerely to impacted customers for any inconvenience caused," the firm said in a statement.
Over the weekend, a handful of people posted on social media that they had taken advantage of the mistake and ordered laptops.
But according to consumer rights group Citizens Advice, retailers can often cancel online orders if they have made a "genuine and honest mistake on their part that you should have noticed".
HP said buyers would be refunded.
"We can confirm that due to a processing error, select products were wrongly priced on our UK website over the weekend," HP said.
"This has now been corrected with related orders cancelled."

Watson, 23, beat Croatia's Ana Konjuh 7-5 4-6 6-3, while Bedene, 26, defeated France's Kenny de Schepper 6-3 6-3. Both are ranked number two in Britain.
However, British number three Naomi Broady went down in three sets to the USA's Christina McHale, 4-6 6-3 1-6.
Laura Robson was knocked out in the first qualifying round on Saturday.
Earlier on Sunday, Dan Evans failed in his attempt to win a second Challenger title in a row, losing 6-4 6-4 to Russia's Konstantin Kravchuk in the final in Busan, South Korea.
The Italian Open is the final major ATP World Tour tournament on clay before the French Open, which begins in Paris on 22 May.
British number one Andy Murray, seeded second, is likely to be in action in Rome on Tuesday.
The 28-year-old Scot - who takes on Novak Djokovic in the Madrid Open final later on Sunday - has been granted a bye in the first round and will meet either Borna Coric or a qualifier in round two.
Listen live to Sunday's Madrid Open final on BBC Radio 5 live sports extra from 17:30 BST
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HP has apologised after an error on its website let shoppers buy expensive laptop computers for less than £2.
[NEXT_CONCEPT]
Britons Heather Watson and Aljaz Bedene are through to the main draw of the Italian Open after victories in the second qualifying round.