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.
Sterling has risen sharply following the High Court ruling on Article 50, while the FTSE 100 has fallen back.