The reformed '90s group played the track during their 22-date arena tour and counted 179,850 people dancing to the track during the shows.
They pushed past the 180,000 figure with a surprise appearance at Sainsbury's in Crayford.
Band member Claire Richards said: "Supermarkets are filled with guilty pleasures to tempt shoppers, and yesterday we were one of them!
"Fans and foodies danced their hearts out, topping off what has been a phenomenal - and now record breaking - tour."
Steps' World Record advisor Thomasina Gibson added: "It was amazing to see so many shoppers putting the brakes on their shopping trolleys to join in the dancing extravaganza.
"Their new DVD Steps: The Ultimate Tour Live is proof that thousands joined in to 'Tragedy', and I'm confident that their supermarket finale will have them stepping up for a world record title."
Steps: The Ultimate Tour Live is out on Blu-ray and DVD now.
Extras include tour director and choreographer Gareth Walker's infectious Learn the Steps Bonus Feature.