Deaths of lung cancer patients from chemotherapy were also far higher than the national average in Blackpool, Coventry, Derby, South Tyneside and Surrey and Sussex, according to the research.
Similarly, around one in five people who underwent palliative care for breast cancer at Cambridge University Hospitals died from their treatment.
Public Health England (PHE), said it had contacted the hospitals concerned to ask them to review practices.
Dr Jem Rashbass, Cancer Lead for PHE, said: "Chemotherapy is a vital part of cancer treatment and is a large reason behind the improved survival rates over last four decades.
"However, it is powerful medication with significant side effects and often getting the balance right on which patients to treat aggressively can be hard.
"Those hospitals whose death rates are outside the expected range have had the findings shared with them and we have asked them to review their practice and data."
The study looked at more than 23,000 women with breast cancer and nearly 10,000 men with 9634 non-small cell lung cancer who underwent chemotherapy in 2014. Of those treated 1,383 died within 30 days.
Chemotherapy is toxic for the body because it does not discriminate between health and cancerous cells.
The researchers also found that there were significant differences in survival for older people and those in poorer health. They advised doctors to be more careful in selecting patients for treatment where it could do more harm than good. "The statistics don't suggest bad practice overall but there are some outliers," said Professor David Dodwell, Institute of Oncology, St James Hospital, Leeds, UK.
"It could be data problems, and figures skewed because of just a few deaths, but nevertheless it could also be down to problems with clinical practice.
"I think it's important to make patients aware that there are potentially life threatening downsides to chemotherapy. And doctors should be more careful about who they treat with chemotherapy."
Professor David Cameron, Edinburgh Cancer Centre, Western General Hospital, Edinburgh, Scotland, added: "The concern is that some of the patients dying within 30 days of being given chemo probably shouldn't have been given the chemo. But, how many ? There is no easy way to answer that, but perhaps looking at those places/hospitals where the death rate was higher might help.
"Furthermore, if we give less chemo then some patients will die because they didn't get chemo. It's a fine balance and the more data we have the better we can be at making sure we get the balance right."
Professor Peter Johnson, Cancer Research UK's chief clinician, said: "Chemotherapy is an important part of treatment for many people with cancer. Having information about how well it is being delivered is vitally important to patients and to the health service."
All the hospitals named said they had since reviewed the cases and were satisfied that chemotherapy prescribing was safe.
The research was published in The Lancet Oncology.