The pound was up 1% at $1.2421 in the wake of the decision, but the FTSE 100 shed 16 points to 6,821 points.
The court ruling has "made triggering Brexit a lot trickier and has given sterling a massive shot in the arm," said Neil Wilson at ETX Capital.
The Bank of England's latest inflation report, released at midday, could also affect sterling.
The Bank is also expected to leave interest rates on hold at 0.25%, but should raise its forecast for UK economic growth and inflation.
The pound also climbed 1.3% against the euro to â‚¬1.1232.
Connor Campbell of Spreadex said that the ruling will be challenged in the Supreme Court next month.
"Even if it does go to a parliamentary vote, it is unlikely MPs will want to be seen as going against the referendum result by blocking the enacting of Article 50. Nevertheless the pound was due some good news, and it has certainly taken advantage of this brief glimmer of hope," he added.
The biggest riser on the FTSE 100 was Royal Bank of Scotland, up 6.3%, while Randgold Resources was the biggest faller, shedding 6.7%.
Shares in Morrisons, rose 2.1% after the UK's fourth-largest supermarket reported another rise in sales.
Underlying sales rose 1.6% in the third quarter, meaning the chain has now reported four consecutive quarters of growth.

UCU, NUS Wales and Unison Wales said those elected following May's election needed to invest or risk denying opportunities for people in disadvantaged areas.
The unions will meet on Monday at University of South Wales in Cardiff to launch the Don't Cut Me Out campaign.
They added most adults returning to study did so without employer support.
Ebbi Ferguson from NUS Wales said: "Our colleges and universities offer a vital second chance to adults who want to develop their skills and to those from disadvantaged communities.
"Cutting funding for post-16 full-time and part-time education denies these people, the majority of whom are women, another opportunity and means there is a huge untapped resource of potential Wales is missing out on."

Tony Aitken, 33, formerly of Melton Mowbray, lost control of his truck on 4 May and his son Luke was thrown from the vehicle.
The boy was celebrating his 12th birthday when he died at Langar Industrial Unit, in Nottinghamshire, police said.
He died later from injuries sustained when the truck fell on top of him.
The truck had three children in the front seat, despite the vehicle only being meant to hold two passengers, Nottingham Crown Court heard.
The other children in the vehicle, aged 12 and five, were treated in hospital for minor injuries.
Aitken pleaded guilty to driving whilst unfit and causing death by dangerous driving and was jailed for five-and-a-half years, Nottinghamshire Police said. He was also disqualified from driving for seven years.
Sterling has risen sharply following the High Court ruling on Article 50, while the FTSE 100 has fallen back.
[NEXT_CONCEPT]
Three trades unions have joined forces to urge assembly members to commit to funding post-16 education.
[NEXT_CONCEPT]
A tipper truck driver has been jailed after the lorry he was driving rolled, killing his son.