The ruling means Prime Minister Theresa May's government will now need MPs' approval before triggering Article 50 -- the mechanism for Britain leaving the EU.
The ruling could give the 48% of British voters who wanted to remain in the EU a greater voice in Brexit plans.
But what do the 52% who voted Leave think about it?
CNN spoke to Brexiteers in Havering, a London borough where 70% of people voted to exit the EU, making it one of the places with the highest percentage of Leave voters across the UK.
Here's what they said.
Disillusioned: The small business owner
Graeme Gibbons, 50, owner of Penny's household goods stall in Romford Market for 25 years.
"People voted for Brexit in good faith and now they're being told that it may not go ahead -- so I think they'll be feeling pretty disillusioned and cheated," said Graeme Gibbons, who voted for "Leave."
"What's the point in having a referendum if they're just going to overrule it anyway?"
Gibbons warned that the sense of injustice among Leave voters could also play into the hands of right-wing parties such as UKIP, which campaigned heavily for tighter immigration controls.
"If we vote in a certain way and it's taken away from us, parties such as UKIP could really capitalize on that sense of dissatisfaction," he said.
"The majority of people voted to leave, it cost a lot of money to hold the referendum, and now they'll be asking, 'What's the point?'"
Disappointed and angry: The clothes vendor
Tony Geary, 49, chairman of the Romford Market Traders Association.
"I voted to get out of the EU," said clothing store owner Tony Geary. "And there was no suggestion that we'd need to go through parliament to get all the necessary boxes ticked before that happened."
"As a small business owner I believed Brexit would be best for my country, and I want the government to fulfill what I've asked them to do."
Geary added that it wasn't just Leave voters in Havering who would be feeling disappointed by the court ruling -- but the majority of the country.
"The referendum was: 'Do we stay or do we go?'" he said.
"Not: 'Let's decide and then we'll get the courts to rule on it and put it another way.'"
Confident Brexit will go ahead: The fishmonger
Dave Crosbie, 58, owner of "The Better Plaice" seafood stall in Romford Market.
"We voted to come out of the EU, so they can't really go against that, can they?" said Dave Crosbie, who believes parliament will keep to Prime Minster Theresa May's deadline for triggering Article 50.
"As long as they stick to the March 2017 date, and don't try and do a backdoor turnaround, I don't think it'll make a huge difference."
Crosbie says he voted to Leave the EU partly because of high levels of immigration -- and hopes any Brexit deal would honor those concerns.
"Tighter immigration control and control over our armed forces -- those things are not negotiable," he said.
"At the end of the day it's the people that voted on it -- so I would hope parliament is fair and gives us voters what we want."