An estimated 400,000 people in England alone are thought to be suffering from conditions such as Alzheimer’s without knowing it.
Studies suggest that up to 800,000 people in the UK are living with dementia, a figure expected to double in the next 30 years.
Yet less than half of them have ever been formally diagnosed, meaning that they miss out on vital treatment and support.
Many of those without diagnosis will be in the early stages of conditions which can take up to 15 years to develop.
The campaign comes as an international study found that the stigma surrounding mental illness meant that people were more reluctant to talk about dementia than conditions such as cancer.
Polling involving people in 78 countries by the charity Alzheimer’s Disease International found that 60 per cent of sufferers lost contact with friends and experienced greater isolation after developing the condition.
As a result nearly one in four said they had deliberately kept their diagnosis a secret for fear that they would be treated differently, the study to coincide with World Alzheimer's Day found.
Separate polling for the Department of Health in the UK showed that 50 per cent of people admit they would struggle to talk about dementia to a friend or relative they suspected might be suffering from it.
Almost two thirds said they would not be confident telling the difference between the signs of dementia and common traits of ageing.
A campaign, backed by celebrities such as Sir Michael Parkinson, the interviewer, includes advertisements highlighting some of the potential warning signs and encourages people to visit their GP.
“Shockingly, nearly 400,000 people are unaware that they have the condition and so we want to make sure more people know what dementia is and how to spot those telltale signs,” said Mr Cameron.
Norman Lamb, the care minister, said: “Dementia is one of biggest challenges we are facing, but while there remains no cure, early diagnosis can help people take control of their condition and plan for the future.
“This campaign sends a clear and important message – if you have spotted signs or symptoms in your loved ones then have that difficult conversation because diagnosis makes a difference.”
Jeremy Hughes, chief executive of the Alzheimer’s Society, said: “At a time when they need more support, people with dementia are still coming up against closed doors and turned backs.
“While this wall of stigma might seem insurmountable, we are beginning to break it down.
“With only 43 per cent of people with dementia in the UK having a diagnosis, it is vital we also tackle the stigma and misunderstanding that is preventing people discussing their concerns or going to their GP.”