A long-running legal battle over whether the NHS should pay for a woman to have surrogate children in America after failing to spot her cervical cancer is due to be heard by the UK’s highest court.

Whittington Hospital NHS trust has admitted negligently failing to detect signs of cancer for more than four years, which led to the woman – known only as XX for legal reasons – developing highly invasive cancer that required chemo-radiotherapy treatment, leaving her infertile at the age of 29.

She was awarded £580,000 in damages to cover the costs of fertility treatment, cryopreserving her eggs and having children by surrogacy in the UK.

The high court refused to award damages to cover the costs of four commercial surrogacies in California as the practice is illegal in the UK.

But in a landmark ruling last December, the court of appeal said XX was entitled to as much as an additional £560,000 to cover the cost of having children with commercial surrogates in the US.

Her solicitors, Irwin Mitchell, said the ruling was the first time the costs of surrogacy in the US had been awarded in a claim for clinical negligence.

On Monday a panel of five supreme court justices in London will hear the trust’s appeal against the damages award.

The case will be the supreme court president Lady Hale’s last hearing before her official retirement in January.

In a statement before the hearing, XX’s solicitor, Anne Kavanagh, said: “This is a tragic case where, due to no fault of her own, my client has suffered grievous injuries including infertility at a young age.

“It is more than a decade since her first smear test was wrongly reported by the Whittington hospital. Her only hope of becoming a mother is by surrogacy, using her own eggs which were harvested just before she started chemo-radiotherapy, as well as using donor eggs.

“The court of appeal granted her the costs of that treatment in California where she will have the security of a legally enforceable agreement to protect her as well as the surrogate and the baby in the event of any dispute, something which would not be available to her under English law.

“Expert psychological evidence supports our client’s case that she will struggle to cope with the uncertainty of the UK system, particularly given that none of this was her choice. We now ask the supreme court to confirm that the court of appeal’s judgment was correct in law so that she can begin to move on with her life once and for all.”