The judgment of the High Court in the matter of the UK leaving the EU can be read in its entirety here.
The last paragraph is the most significant:
In their prior argument the judges state that leaving the EU will result in British citizens losing certain rights, and only Parliament can take away people's rights. Clearly none of us would want to have a system where the government could cancel your rights by decree.
But the judgment is none-the-less flawed, because Parliament is not the supreme sovereign law-making body: the People are. Parliament derives its authority by being elected by the People and is therefore subordinate to the People collectively.
Their Lordships are wrong because they give no weight to the Will of the People as expressed by Referendum. In voting for Leave the People have voluntarily given up such rights that they may lose in the process (and of course, depending on negotiations they may not actually lose any rights) so the government is not cancelling rights by decree but rather is exercising a power conferred by the referendum.
Some might argue that since the Referendum Act which brought about the referendum does not confer such a power, the power does not exist, but that is to make the same mistake twice. Parliament cannot confer power on itself; nor can it remove power from the People. Once the referendum has happened and the Will of the People expressed, the matter becomes decided and Parliament is bypassed because of its inferior status.
This blog rules that the Secretary of State does have the power to trigger Article 50.
There are a couple of other interesting points:
1) The Court is the High Court of England and Wales, its judgments do not apply in Scotland. The Secretary of State (for Brexit, David Davis, MP) could still trigger Brexit from Scotland. However the government intends to appeal to the UK Supreme Court - which does cover Scotland. So if they lose there that option goes away.
2) The judgment only binds the Secretary of State; the Prime Minister still has a free hand. However, it not likely she will defy the Court by doing the deed. No, her plan is likely: appeal to the Supreme Court, and if that fails, pass an Act in Parliament, and if that fails - General Election.