Others will be starting soon.
As the Department of Health formally launches the seasonal flu immunisation campaign today, Dr Alison Barnett, Director of Public Health for Medway, said: "For most of us, flu is inconvenient, but for some people, it's much more serious. More than 600 people across the UK are known to have died as a result of flu last year, including nine pregnant women.
"In 2009, more people died from influenza and pneumonia than died with breast cancer or prostate cancer.
"Vaccination is the single best protection against flu for those people who are most at risk.
"I would urge everyone who is eligible for a flu jab to act now and make sure they are protected against flu this winter."
Last year, many people, who did not attend routine flu clinics at their GP practice, urgently sought immunisation in December when flu infection rates soared. This delay put them at risk of becoming very unwell.
The vaccine is modified each year to match the flu strains in circulation. This year, it again protects against the H1N1 virus (swine flu) along with two other strains that will be circulating this winter.
Pregnant women and young and middle-aged people who already have a serious health condition are at particular risk of becoming very ill if they catch H1N1, which caused the majority of deaths of last winter.
People who are eligible for the flu jab are pregnant women, people with long-term conditions such as heart disease, diabetes, asthma, multiple sclerosis, serious kidney disease, and liver disease, people who have lowered immunity (because of illness or treatment for illness) and people over 65. People who are the main unpaid carer for someone who depends on them are entitled to free vaccination.
Prevention is also an important part of the fight against flu.
"The best way to stop the virus spreading is by good hand hygiene," said Dr Declan O'Neill, Director of Public Health Improvement for Kent. "Use a tissue to catch coughs or sneezes, throw it away and wash your hands - remember catch it, bin it, kill it."
For more information, see www.nhs.uk/winterhealth. If you think you may have flu, check your symptoms online at www.nhsdirect.nhs.uk. For any health worries or concerns, you can phone NHS Direct round the clock on 0845 46 47.