Dr Granger, who was 34, pioneered the #hellomynameis campaign to improve patient care.
She had been diagnosed with cancer at the age of 29 and told that she was incurable after the disease was discovered to be desmoplastic small round cell tumour.
She also raised some £250,000 for a Yorkshire cancer charity.
The NHS runs an annual award for patient care in her name - and the latest winners are due to be announced in the autumn.
She had worked at Pinderfields Hospital, Wakefield, and wrote two books about her experience as a patient.
She had set out to achieve a list of ambitions during her remaining years, including qualifying as a consultant in elderly medicine, and sky-diving. She was awarded an MBE.
Last week she tweeted: “Sorry for the distinct lack of #deathbedlive tweets. I've not had the energy. I'm so grateful for everyone’s support, messages & presents. "
Her husband Chris Pointon announced her death on Twitter, saying: "Peacefully & surrounded by loved ones @grangerkate passed away yesterday. RIP my soul mate & TY (thank you). Love u 4ever..."
Hundreds of Twitter users used the hashtag #hellomynameis to pay tribute last night.
Health secretary Jeremy Hunt - who she had criticised for his treatment of junior doctors - was among those to pay tribute. He said: "Her legacy promoting a more human touch and compassionate care will outlive us all."
Scottish chief minister Nicola Sturgeon tweeted: "Kate made a real and lasting difference. Be proud of her."
Danny Mortimer, chief executive of NHS Employers, said: “Kate used her experiences to pioneer the #HellomyNameis campaign to remind staff to see patients as people.
“The campaign has been adopted across the country, making a huge difference to patients. It will be a profound legacy of her work, along with the Kate Granger Compassionate Care Awards and the countless people she has inspired with her example.
“She had humility, compassion and warmth in equal measure and will be greatly missed."
GP leaders say doctors are struggling to help women affected by these problems within the standard ten-minute consultation.
The Royal College of GPs is now offering a "one stop" hub with resources to give doctors quick access to information.
Dr Carrie Ladd, a clinical fellow for perinatal mental health, said: "We recognise that GPs are under immense workload pressures at the moment – and the standard ten minute consultation is increasingly inadequate to properly deal with complex issues associated with perinatal mental health.
"We hope this collection of resources will enable GPs and other members of the primary care team to access information quickly and within the consultation so helping them offer the best possible care to their patients at this important time in their lives."
She added: "I know from talking to GPs and patients in my practice, and via support groups on social media, that there is a real need for more to be done around perinatal mental health.
“It has been developed in consultation with women who have had perinatal mental health problems, and we hope it will give them the confidence to approach health professionals, and be better informed about their choices and what they should expect."
Dr Judy Shakespeare, who champions the problem at the college, said: “While our attitudes to mental health issues seem to be improving as a society, a terrible stigma still surrounds mothers with mental health problems, not least from the women themselves who think they are being judged as 'bad' mothers or are frightened that their child will be taken away if they open up about how they are feeling."
The disease is known as lung disease immunodeficiency chromosome breakage syndrome, the researchers have announced.
Families carrying the genetic variant behind the disease have been found in the Netherlands and in the USA. Both families lost two infants to the condition.
The discovery has been announced in the Journal of Clinical Investigation.
It involved the genome damage and stability centre at Sussex University, the University Medical Centre, of Utrecht, Netherlands, and Baylor College of Medicine, Houston, USA.
The research links the condition to the gene NSMCE3 and to defects in the levels of Smc5/6 proteins, which are needed for the copying and repair of DNA.
Researcher Dr Jo Murray, from Sussex, said: “This international study shows that collaboration between clinicians and research scientists is key to understanding what is going on in the cells and the development of diagnostics tools.
“The mutation we’ve discovered in the NSMCE3 gene is rare but mutations in related genes could lead to similar tragic outcomes – which is why it is so important that we now work to develop a clinical test that can be used to identify families at risk.”
Dr Gijs van Haaften, from Utrecht, said: “Now we can provide a scientific explanation to the families, hopefully improve diagnostic opportunities for future children with a similar disease and understand more of the function of the DNA repair complex in the human body in health and disease.”
Destabilized SMC5-6 complex leads to chromosome breakage syndrome with severe lung disease JCI 18 July 2016 [abstract]
Patients with serious mental health problems mostly interact with professionals in this field.
Researchers at City University, London, found that mental health workers tended to think that patient diabetes was not their responsibility.
Reporting in BMC Psychiatry, researchers found wide ignorance of how to manage and monitor type 2 diabetes - describing this as a "significant barrier."
They found poor awareness of national and local guidelines for managing diabetes.
The research involved four psychiatrists, three GPs, a diabetologist and nine nurses.
Researcher Professor Alan Simpson said: “There is a hidden diabetes epidemic impacting on the lives of people with serious mental illness, as thousands of people with schizophrenia and bipolar disorder – along with other psychoses - are not having their diabetes properly managed, often causing complications which could have been avoided.”
He added: “What we need to do is address the fact that diabetes is up to three times more likely in those with such mental health conditions, and therefore we need a comprehensive rethink about how we properly manage their mental and physical health in a way which ensures a high quality of care.
"To do this effectively interventions need to be targeted at both an organisation and individual level in order to change behaviour and increase knowledge and understanding.”
Implementation of recommended type 2 diabetes care for people with severe mental illness – a qualitative exploration with healthcare professionals. BMC Psychiatry 8 July 2016; doi: 10.1186/s12888-016-0942-2 [abstract]