The campaigners share similar aims as the Women Against State Pension Inequality (Waspi) who claim they did not know about plans to delay their pensions and that communication over the changes from the government were badly handled.
The groups claim that the 1995 and 2011 Pension Acts were implemented unfairly, giving the women little or no time to make alternative plans.
The state pension age is now 65 for men and women, and will rise steadily to 67 by 2028
The BackTo60 group is calling for all women who were born in the 1950s to be given the same amount of state pension as they would have received had it started at the age of 60. The government has said this would cost more than £70 billion and has ruled out the idea.
The judicial review was being sought claiming the pension policy of successive governments “constitutes a gross injustice and is discriminatory”.
Jackie Jones, law professor at the University of the West England, said there could be legal grounds for the state pension age hike for women to be removed and for full restitution.
A date has yet to be set for the next stage of the legal challenge.