Societies that consume more products with animal fat tend to have higher risks of heart disease, the consultant cardiologist at the London Chest Hospital told ITV News.
Dr Charles Knight recommended people to adopt a Mediterranean diet, which is "rich" in olive oil, fruits and nuts.
The government should consider “proper regulation” to tackle high levels of saturated fat, say campaigners.
Tam Fry, trustee of the National Obesity Forum, added: "This latest piece of hype from the Department of Health will still mean over 50% of food will still have extreme levels of saturated fat.
"The much vaunted voluntary Responsibility Deal will never succeed until the Government takes a grip and makes everybody sign up to it."
Labour public health spokeswoman Luciana Berger says the government’s attempts to reduce saturated fat in supermarket food has little chance of succeeding.
She said: "A few company names on a non-binding plan with no timescale stands little chance of delivering the fundamental change needed to improve our national diet.
"Labour has put forward bold ideas to set legal limits on our food's fat, sugar and salt content and achieve a cross-party ambition for a more physically-active nation."
Kit Kat chocolate bars will not taste any different despite a new recipe with less saturated fat, according to a spokesman for Nestle. The firm, which manufactures Kit Kats in York, has signed a government pledge to reduce the amount of saturated fat in the UK diet.
Michelle Roberts, the company's Head of Nutrition, said the firm has spent three years researching the new recipe.
Public Health Minister Jane Ellison has praised firms including Sainsbury's, Tesco, Morrisons and Nestle for committing to reduce saturated fat in products as part of a new ‘responsibility deal’.
One in six male deaths and one in nine female deaths are from coronary heart disease - this is why it's critical that we challenge the way we eat and that we all make changes where we can.
It's hugely encouraging that companies providing almost half of the food available on the UK market have committed to this new Responsibility Deal pledge and they are leading the way to give their customers healthier products and lower fat alternatives.
Sainsbury's, Tesco and Morrisons have pledged to reduce saturated fat from a number of products after a new health warning.
A new poll by Sainsbury’s suggests 84% of adults have no idea how much saturated fat they should eat a day.
Other companies are also on board, with Nestle promising to change the recipe of its Kit Kat bar.
The vast majority of adults have no idea how much saturated fat they should eat every day, a poll suggests.
Eighty four per cent of adults do not know that men should eat no more than 30g of saturated fat each day and women should eat no more than 20g, the survey found.
The poll, conducted by supermarket Sainsbury's, also found that one in five adults think that all types of fat are bad for one's health.
Tesco has said the challenging retail environment in Europe continues to affect its performance, as it reported a 23.5% drop in group pre-tax profits to £1.39 billion in the six months to August.
Chief executive Philip Clarke told ITV News: "There are always bumps in the road and the Eurozone is one of those and it's been an extraordinary impact since 2008."
But he added: "We feel we've got every opportunity to grow and make progress".
Tesco has revealed that its trading profits in its UK business rose 1.5% to £1.13 billion, with like-for-like sales excluding petrol remaining flat in its second quarter after falling 1% in the previous three months.
Despite improved trading in the UK, the retailer's first half group pre-tax profits of £1.39 billion, are down 23.5%.