But women say the exemption does not easily apply to them because their first two children, born as a result of rape, were born before their third or more children born from consensual relationships.

The Child Poverty Action Group (CPAG) provides legal representation for women and says the policy is “discriminatory and unreasonable”.

Claire Hall, the charity’s head of strategic litigation, said: “They should be able to get exemptions for children conceived without consent, regardless of at what point they are born.”

One of the women, known only as LMN, took action against the Department for Work and Pensions (DWP) in the High Court and eventually received benefits for her third child.

“He has lived without this support for many years, amounting to thousands of pounds, and this support will not be retroactive,” CPAG said.

The second woman, known as EFG, made a statement via CPAG: “If I had been raped after my first two children were born, exceptions would have been made.”

CPAG says both women have missed out on thousands of pounds of support because of the current policy.

A DWP spokesman said: “We cannot comment on ongoing legal proceedings.”

The Supreme Court trial is expected to take place next year.

The two-child limit came into force in April 2017 and was opposed by anti-poverty campaigners.

A DWP spokesman said at the time: “We have always been clear that this will be delivered in the most effective and compassionate way, with the right exceptions and safeguards.”

The spokesman was unable to explain how to substantiate claims made by a woman who never accessed support or told anyone she had been raped.

In 2023, Sir Keir Starmer told the BBC that a Labor government would not change the two-child limit and spend extra money on benefits without growing the economy first.

In the past, campaigners have lodged a legal challenge to the High Court against the two-child limit, arguing it violates the human rights of parents and children; this case was dismissed in 2021.