According to London School of Economics researchers, more than 100,000 people a year who would benefit from palliative care are not getting it.
Patients are being left without sufficient pain relief and respite.
NHS England said it was committed to ensuring terminally-ill patients got the support and services they needed.
The report found inequalities in access to good care, with certain groups of patients more likely to miss out.
With an ageing population and demand for care increasing, the problem looked set to worsen, it warned.
Those who currently miss out include:
Most palliative care goes to cancer patients, even though the diseases account for less than a third of deaths.
Only a fifth of new referrals to specialist end-of-life services are for people with non-cancer diagnoses.
According to the report, commissioned by the Marie Curie charity, providing palliative care to those that need it could improve the quality of life for thousands of patients and save the NHS money by preventing unwanted and distressing hospital treatment.
By their calculations, the net potential savings are more than £30m in England, at least £2m in Wales, more than £1m in Northern Ireland and more than £4m in Scotland.
Meanwhile, a separate MORI poll of 500 health professionals who look after terminally-ill patients - also commissioned by Marie Curie - reveals that many feel there is insufficient funding and staffing to provide the level of care needed.
Likewise, a recent poll of 1,067 carers - mostly family members, friends or neighbours of terminally-ill people - felt the current care system did not offer enough support.
Denis McKnight, 68, from Northern Ireland, cared for his wife, Georgina, who had motor neurone disease.
A district nurse would visit once a week, but Mr McKnight said this was nowhere near enough to meet their care needs.
He said: "I felt alone. I felt almost abandoned, except for my family.
"Palliative care as it is provided by the nursing system is the best that they can possibly do. Most nurses would want to do the very best job possible. They just don't have the resources to do it.
"It's the system that is cracking under the strain."
When Mr McKnight struggled to cope with his wife's increasingly demanding care needs as her disease progressed, a friend suggested he ask Marie Curie for help.
Mrs McKnight was unable to walk or move for herself and could not swallow, so needed to be fed via a tube.
Mr McKnight said: "I'm more than grateful for what Marie Curie did, even for that short period of time. They stepped in as specialists and gave specialist help.
"They were able to step into the breach - a breach that's been created through lack of resources in the ordinary healthcare system."
Dr Jane Collins, chief executive of Marie Curie, said: "Everyone affected by terminal illness should have access to all the care and support they need, regardless of their personal circumstances. This report shows that this is not the case, and some groups are getting a worse deal than others. We don't think this is good enough."
Katherine Murphy, chief executive of the Patients Association, called the current situation a "national disgrace".
"These findings mirror many of the inquiries to our national helpline. It is unacceptable that we continue to fail the most vulnerable in our society."
Dr Bee Wee, national clinical director for end-of-life care at NHS England, said: "NHS England is committed to ensuring that all patients get the support and services they need towards the end of life."
A Welsh government spokesperson said: "Whether a person wishes to die in hospital, in a hospice or at home, we want to make sure the right level of professional, caring support is available.
"Ensuring that care and support is effectively planned and co-ordinated across health and social care to meet people's needs is one of the priorities being taken forward through our work on integration."
The UK's care system for dying patients with terminal illnesses is lacking and needs a major overhaul, says a damning new report.