Despite survival rates generally improving across Britain, the country still performs worst for major cancers including bowel, lung and pancreatic.
Cancer Research UK analysed 3.9 million cancer cases between 1995 and 2014 in seven high-income countries which benefit from universal healthcare: Australia, Canada, Denmark, Ireland, New Zealand, Norway and the UK.
The data covered cancer of the oesophagus, stomach, colon (bowel), rectum, pancreas, lung and ovary.
The UK only showed better survival rates in two of the seven types - oesophageal and ovarian.
The authors of the study, published in the journal Lancet Oncology, said the differences between the countries was partly explained by how quickly patients get a diagnosis and then prompt access to effective treatment.
Cancer Research UK's clinical adviser and the study’s co-author John Butler said: "For lung, ovarian, and oesophageal cancer in particular, survival has increased largely because the quality of surgery has radically improved, and more surgery is taking place than before.
"More people are being looked after by specialist teams, rather than surgeons who aren't experts in that area.
"But, while we're still researching what can be done to close the survival gap between countries, we know continued investment in early diagnosis and cancer care plays a big part.
"Despite our changes, we've made slower progress than others."
Cancer Research UK's director of early diagnosis Sara Hiom urged the government to correct staff shortages across the NHS and address late diagnosis.
She said: "We will not see the necessary improvements in diagnosis and access to treatment unless we have enough of the right staff across our NHS.
"Cancer Research UK has been calling for staff shortages to be addressed because, quite simply, it will give people a better chance of surviving their cancer."
However, the Government has celebrated data showing that one-year survival rates for all types of cancer are at a record high.
The latest figures for England show that one-year survival increased from 62 per cent in 2001 to 72.8 percent in 2016.
A Department of Health and Social Care spokesman said: "Cancer survival rates are at a record high, but we are determined to go further and save even more lives.
"Through our NHS Long Term Plan, we will detect more cancers at an earlier stage, saving an estimated 55,000 lives a year.
"Alongside this, the record £33.9 billion extra a year we're investing in our NHS will help support the health service in recruiting the staff it needs for the future."
An NHS England spokeswoman said the report was out of date and pointed to the increase in one-year survival rates seen in England.
She said this was "thanks to improvements in NHS cancer services, including the introduction of revolutionary treatments like proton beam therapy and immunotherapy".
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Data shows that three-quarters of NHS services are failing to treat cancer patients quickly enough.
Hospitals are meant to start treatment within 62 days of an urgent referral by a GP.
But 94 out of 131 cancer services in England failed to do that between 2018-19 compared with 36 five years ago, BBC analysis has found.