The campaign, launched today by fertility charity the Progress Educational Trust (PET), has been prompted by anger over the timescale by which women have to use the eggs they have had frozen.
This means that many are forced to make a life-changing choice irrespective of their circumstances.
Under the Human Fertilisation and Embryology Act 1990, women who freeze eggs for non-medical reasons can store them for only 10 years. They then have to use them, destroy them or transfer them to a fertility clinic overseas.
The campaign is seeking to extend this limit by forcing the government to debate the issue at Westminster as a step towards changing the law.
A key message is that women should have a choice over having children, but many have to decide whether to destroy their frozen eggs or become a mother before they are ready because of an outdated and unscientific law.
The campaign is also seeking to persuade people that the current law breaches human rights, curtails women's reproductive choices, and is an arbitrary and outdated piece of legislation.
Another core message is that the 10-year limit is a perverse incentive for women to delay freezing their eggs until later in life, when egg quality may have declined – reducing their chances of conceiving.
A mix of traditional and social media are being used in the campaign, which is targeting men and women aged 18-55 and will continue until there is a change in the law.
Social-media engagement, website hits and political progress will be used as measurements of its impact.
Referring to the campaign petition, Dr Catherine Hill, head of communications, PET, said: "At 100,000 signatures the Government will be forced to debate a change in the law at Westminster. Just a minor amendment would remove this cruel and pointless legislation and give so many women hope for a fertile future."
And Sarah Norcross, the charity’s director, described the 10-year limit for egg freezing as "a very clear breach of human rights."
A number of individual case studies, including TV presenter and scientist Dr Emily Grossman, are being used in the campaign.
It also has high-profile supporters such as Baroness Ruth Deech QC, former chair of the Human Fertilisation and Embryology Authority, and Professor Emily Jackson, specialist in medical law at the London School of Economics.
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