Although there is no rule preventing any woman from having her eggs stored, the process is only currently freely available to cancer patients, who may wish to freeze their eggs in case their treatment makes them infertile.
Just 20 babies in the UK have been born from frozen eggs, despite the fact that storage has been available for a number of years.
The call comes as more and more women delay having a family, often because they want to extend their careers or because they haven't found the right partner.
Josephine Quintavalle, director of Comment on Reproductive Ethics (CORE), told Premier: "I don't think the solution is to say we'll freeze your eggs, because that's no guarantee that you'll be successful.
"Egg freezing and deep freezing and all the manipulation that goes on, and IVF doesn't guarantee you a child, so I think it will be giving women false hope.
"I think it's nature's way of endorsing the value of a woman's contribution to bringing up children. This idea that you can have a child at any stage and you'll always have the energy to bring up the children...is kind of nonsense.
"We're hearing all the time about the NHS being strapped for cash and all the rest of it, and suddenly we're going to consider it's legitimate to spend money on storing eggs."
Experts say the treatment can cost up to £8,000.