The recurrence of cancer was also reported to be low
The cancer is usually treated by an operation to remove the cervix and the womb, leaving the woman unable to have children.
But two London hospitals are offering less radical surgery which has had success in treating the disease without destroying the essential parts of the reproductive system.
Specialists at St Bartholomew's Hospital and the Royal Marsden Hospital have published a report of the new treatment on a group of women and their lives after surgery.
Surgeons removed just the cervix and a smaller amount of tissue from the patients, leaving the womb intact.
Low recurrence
The report showed that a number of patients went on to conceive naturally and have children delivered by caesarean section.
The recurrence of cancer was also reported to be low, with only one case out of 50 women who have had the operation so far.
John Shepherd, a professor of obstetrics and gynaecology at St Bartholomew's, told the Sunday Telegraph the success of Britain's cervical cancer screening programme meant that the disease was being caught in its early stage in many more patients.
He said it was time to consider whether they all needed drastic treatment that would leave them infertile.
"The traditional treatment for cervical cancer is a radical hysterectomy or radical radiotherapy but that of course takes away all the hope of having a baby and a family," he said.
"What we are trying to do is to conserve that."
Doctors believe the technique could help a carefully selected group of women in the early stages of cancer, where the disease is small and unlikely to have spread.
The report is to be published in next month's British Journal of Obstetrics and Gynaecology.