Unite the union was seeking leave to appeal against the ruling on Monday that rendered its strike plans illegal.
However, the government has decided to appeal against the ruling on the grounds of "public health".
The state attorney refused to file the case and appealed against the ruling.
The four defendants have already announced their intention to appeal against the ruling, a process which could take as long as two years.
BT announced that it would not appeal against the ruling.
Protect Marriage, the coalition of religious and conservative groups that sponsored the ban, said it would immediately appeal against the ruling.
Nina appealed against the ruling but lost in a 2-1 decision on 28 June 2004.
However, Silvertone appealed against the ruling, delaying the record for another year.
Watson has appealed against the ruling and refused to provide the court with an inventory of Tina's possessions.
Both sides have three months to appeal against the ruling to the Grand Chamber of the court - its highest decision-making body.