The group includes carers as well as people with a range of underlying health conditions that put them at greater risk from coronavirus.
They include chronic respiratory, heart, kidney and liver disease and neurological conditions, immunosuppression, asplenia, diabetes, morbid obesity and severe mental illness.
People with sickle cell disease, lupus and those on a GP learning disability register, as well as people who have vascular disease or have had a stroke are also included in group six.
The letter states: “We are writing today to encourage people living with an underlying health condition in cohort 6 to come forward for a Covid-19 vaccine.
“People with these conditions, including their carers and those with learning disabilities on the learning disability register, have been prioritised by the Joint Committee on Vaccination and Immunisation because they are more likely to become seriously unwell from Covid-19.
“The vast majority of you should already have been invited for vaccination and more than half of you have already received your first dose. Some of you may still be waiting for a letter from your GP.
“But the good news is, even if you have not received your letter yet, you can now get an appointment at a vaccination centre or community pharmacy, quickly and easily, by using the national booking system or calling 119 in England.”
More than 23.6 million people have received their first dose of a coronavirus vaccine in the UK, the latest Government figures showed.
There were a further 5,534 lab-confirmed cases of Covid-19 in the last 24 hour period, while 121 deaths were recorded in the UK of people who tested positive for coronavirus in the last 28 days.
Health Secretary Matt Hancock said the backing of the charities was “invaluable” in encouraging more people to come forward for a vaccine.
He said: “The backing of the charities who work every day to support those who are entitled to a jab as part of cohort 6 is a great boost for the vaccine rollout and shows what we can achieve when we pull together.
“This open letter is a hugely important way to reassure those with underlying health conditions, and their carers, about the safety and effectiveness of the vaccine.
“The charities’ support for this national vaccine effort is invaluable in encouraging more people to come forward and helping us to save lives.”
Vaccines Minister Nadhim Zahawi added: “We have already given a first dose of the vaccine to more than half of those in cohort 6 and I am grateful to the charities who are encouraging more people in that group to come forward.
“The vaccine is our way out of this pandemic and offers the chance to protect yourself and others – that’s why it’s vital that people get their jab.
“This open letter should help to reassure those with any concerns the vaccine is safe and supported by more than twenty of our most trusted charities.
“I would like to thank them all for backing this life-saving campaign and offering their expertise and assistance to support the largest medical deployment in British history.”
The letter has been signed by ACLT (African Caribbean Leukaemia Trust), Anthony Nolan, British Liver Trust, Cancer Research UK, Carers UK, Diabetes UK, Epilepsy Action, Kidney Care UK, Kidney Research UK, Lupus UK, Mencap, MS Society, National Kidney Federation, Rethink Mental Illness, Sickle Cell Society, Stroke Association, Terrence Higgins Trust and Versus Arthritis.
Meanwhile, the NHS is to text millions of vulnerable people with underlying health conditions asking them to take up a vaccine “to ensure nobody is left behind”.
The health service will send out around two million texts over the weekend to people with conditions such as diabetes and certain forms of cancer.
They will receive a link to reserve an appointment for a jab at a vaccination centre or pharmacy across England.