The Government's appeal over the High Court Brexit ruling opens itoday.
The Supreme Court will decide this week whether or not to overturn the ruling that the Prime Minister must seek parliamentary approval before triggering Article 50 and beginning to negotiate the exit from the European Union.
The case was won by investment fund Gina Miller, with a panel of three senior judges saying Theresa May lacked the power to use the royal prerogative to trigger Article 50 in a ruling which infuriated Brexiteers.
A panel of 11 justices will rule on the Government's Supreme Court challenge, with the Scottish and Welsh governments and Northern Ireland's attorney general all presenting submissions.
If the Government's appeal is unsuccessful, and any potential further appeal to the European Court of Justice also fails, their Brexit plans could be delayed.
The Supreme Court has already stressed that its appointed judges will only be concerned with questions of law, rather than make political decisions.
The Attorney General said: "The country voted to leave the European Union in a referendum provided for by an Act of Parliament.
"The Government is determined to respect the result of the referendum. The Government's case is that it does have legal power to trigger Article 50 on the timetable set out by the Prime Minister. We do not believe another Act of Parliament is necessary."
The Counsel General for Wales, Mick Antoniw, said: "The people of the UK voted to leave the European Union. I respect that decision and we will not work against the referendum result."
He said: "Leaving the EU will lead to significant changes to the Welsh devolution settlement - only the UK Parliament can make these changes, with the agreement of the National Assembly for Wales."
Brexit Secretary David Davis is leading the Government's unprecedented legal action, and Theresa May has made it clear she still intends to trigger Article 50 to start the leave negotiations by the end of next March.