It shows a sink getting clogged with fat and asks viewers to imagine what the fat they consume is doing to their own pipes.
Posters using food in a heart design will also suggest ways that people can reduce the amount of saturated fat in their diet.
The FSA said UK consumers were eating a fifth (20%) more saturated fat than the government recommended.
Although people say they do know that saturated fat is bad for them, they do not necessarily link it to heart disease and what they are eating, says the FSA.
TIPS FOR CUTTING DOWN
Grill rather than fry meat
Take the skin off chicken and turkey
Cut down cheese by grating it or using stronger flavour
Switch to lower fat spreads
Check food labels for saturated fat content
Virtually all the 3,219 people surveyed in October and November last year the regulator had heard of saturated fat and three fifths (61%) thought they should be getting less saturated fat in their diet.
But only a fifth (19%) said they planned to cut down.
Nearly half (48%) thought that there was no need to worry about how much saturated fat they ate if, for example, they took regular exercise, were not overweight or ate lots of fruit and vegetables.
The campaign is focusing on working class and lower middle class women aged 25 to 60 who are thought to be most likely to change their behaviour.
As women, they are also likely to the be main food shoppers in their household.
The National Diet and Nutrition Survey 2003 found 90% of children, 88% of men and 83% of women eat too much saturated fat.
Women and children aged 5-10 should eat no more than 70g of fat per day and only 20g or less of this should be saturated fat.
Men should eat no more than 95g and only 30g should be saturated fat.
Too much fat in the diet raises cholesterol levels in the blood, which is a risk factor for coronary heart disease, heart attacks, angina and stroke.
Saturated fat contributes to obesity, which carries its own health risks, including certain cancers. But the damage to the body caused by saturated fat is hidden, which is part of the problem.
The FSA's chief executive Tim Smith said: "People say they do know that saturated fat is bad for them but they don't necessarily link it to heart disease and what they are eating. It's important they make that connection, because heart disease is the UK's number one killer - one in three of us will die as a result."
He said there were simple ways to cut down on saturated fat.
COMMON FATTY FOODS IN UK DIETS
Meat and meat products, like pies
Biscuits, buns and cakes
Crisps and similar snacks
"We need to eat leaner meat and a bit less cheese, switch to lower fat milks and eat healthier snacks, cutting down on cakes and biscuits.
"Supermarkets and manufacturers have done some good work so that now when we're shopping there is an increasing range of lower saturated fat foods available and better labelling, and we'd like to see more of this."
Peter Hollins, chief executive of the British Heart Foundation, said: "Empowering everyone with the knowledge they need to make healthier choices in the shops is essential, but so is the commitment of food manufacturers and retailers."
Julian Hunt of the Food and Drink Federation said: "Changing the recipes of much-loved British brands so that they are lower in saturated fat is a complex task, as it needs to be done in a way that does not impact functionality, quality or price.
"But our members have been rising to this particular challenge for a number of years and are now leading the world when it comes to the reformulation of popular products."
Dietician Jacqui Morrell said people needed to think about the foods they buy and eat.
"Many of our favourite dishes including spaghetti bolognaise, chicken curry and even the humble cheese sandwich contain more than 10g of saturated fat per serving - that's over half of a female's Guideline Daily Amount of 20g.
"Combine that with butter on 2 slices of toast for breakfast, which contains 10.8g and you've already exceeded your limit for the day."
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