Jakki Smith, 58, was unable to claim bereavement damages after her partner of 16 years died as a result of medical negligence.
Her initial bid was rejected by a High Court judge, who said he was "powerless" to intervene but hoped Parliament "might improve the current state of the law".
She has asked for permission to appeal.
Ms Smith's partner John Bulloch died in 2011 when an infection which was missed by medics spread to his brain and killed him.
After his death, she discovered she was not entitled to Â£12,980 which is usually paid out in cases of negligence, because she was not Mr Bulloch's spouse or civil partner.
She said her inability to claim damages was a breach of her human rights.
At the High Court earlier this month, Mr Justice Edis said he agreed reform of the law was needed.
"It is to be hoped that the outcome of this litigation may provoke some further discussion in Parliament for further legislation which might improve the current state of the law," he said.
Ms Smith, from Chorley, Lancashire, said: "Bereavement damages are recognition of the pain and grief caused by the death of a partner and I felt that same pain and grief, with or without a marriage certificate."
Her lawyers argued bereavement damages should be extended to people who have lived with their partners for more than two years, as is already the case in Scotland.
Zak Golombeck, of Slater and Gordon, said: "We remain hopeful the courts will address this inequity, which is why we are applying for permission to appeal."
A woman has launched a legal fight to win greater recognition for unmarried couples who suffer bereavement.