Justice secretary Liz Truss said the independence of the judiciary was the "foundation upon which our rule of law is built" after attacks on the legal system following the High Court's ruling on Article 50.
However she did not condemn attacks made on the profession from some Conservative MPs and media outlets in the wake of Thursday's ruling.
"Our judiciary is rightly respected the world over for its independence and impartiality," she said.
"In relation to the case heard in the High Court, the Government has made it clear it will appeal to the Supreme Court. Legal process must be followed."
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A High Court judge has ruled that a preventative treatment for HIV can legally be made available on the NHS.Read the full story ›
Jon Platt won a legal battle after being fined for taking his daughter on a holiday during term-time- but this ruling is to be appealed.Read the full story ›
A heterosexual couple have lost a High Court challenge against a bar to them entering a civil partnership.Read the full story ›
The son of a coke plant foreman has won the right in principle to seek compensation for his father's death from respiratory problems.Read the full story ›
A High Court judge has been criticised for saying that "cultural context" should be taken into consideration when investigating child abuse.Read the full story ›
A woman who lost her husband to brain cancer two years ago has won a legal battle to prevent his frozen sperm being destoyed.
Beth Warren, spoke to ITV's Daybreak programme earlier about how she may have to take her fight back to court again if an appeal is lodged.
Before the fertilisation watchdog announced it was to challenge the High Court ruling, widow Beth Warren had told ITV News she was "elated" at a judge saying she could preserve her late husband's sperm.
She said: "It's absolutely amazing. I knew it could go either way. I am elated.
"Warren's family and friends have told me how proud he would have been of me, and that means a lot.
"Warren was such a fighter, he fought the brain tumor as hard as he possibly could, he stayed positive. We tried and he taught me how to be a fighter."
A widow who won a High Court fight to preserve her late husband's sperm was tonight "downhearted" after the UK fertility regulator was given permission to try to overturn the ruling.
Physiotherapist Beth Warren, 28, from Birmingham, had been "elated" after a High Court judge ruled in her favour following a hearing in London.
But her mood changed when Human Fertilisation and Embryology Authority (Hfea) was given permission to take the case to the Court of Appeal.
"Oh dear," she said. "I thought it was all over."