A number of MPs who backed the assisted dying bill claimed introducing it would help improve palliative care.
They pointed to a report by the Health and Care Committee which found in some countries it had been linked to an improvement.
But Dr Cox questioned this, saying it was a “very mixed picture”.
She added: “We know money is the NHS is finite – and our concern is that palliative care will lose out. The NHS will need doctors to assess patients, and judges to agree. That is all going to cost money, and palliative care is already struggling.”
More coordination between hospitals, community NHS teams, care homes and hospices is needed, and training for non-palliative care specialists is also an issue, she said.
Sam Royston, director of policy at Marie Curie, agreed action was needed on palliative care: “We have taken a neutral position on assisted dying, but we do not take a neutral position on the need for improvement on palliative care.
“The needs of people at the end of life are being neglected. There are no realistic plans currently in any UK nation to improve palliative care.”
He said just because MPs had backed assisted dying, did not automatically mean there would be improvements in palliative care too: “We had asked for a clause within the bill for a strategy around palliative care. If it does pass we will ask for this to be given greater attention.”
But Prof Sam Ahmedzai, a retired palliative care doctor and former NHS adviser on end-of-life care, said he had been to countries where both systems worked well in parallel with each other – and in some places where assisted dying had been introduced, palliative care had been improved.
He suggests more attention and training could be given to the people who provide the most palliative care – often GPs, district nurses and hospital doctors working in different departments.
The Department of Health and Social Care has been approached for comment.