The campaign could affect the bakers which supply bakeries with fresh bread, as they may find themselves coming under tighter regulations in regards to how they bake and package the product.
According to a recent Which? survey, fresh supermarket bread contains, on average, 0.9g of salt per 100g of product. However, the actual figures vary widely - from 0.5g in Asda's granary tin, to 1.1g in some Morrisons, Tesco, and Sainsbury's loaves.
Speaking to BakeryandSnacks.com, campaign group Consensus Action on Salt and Health (CASH) said that supermarkets across the UK should make a concerted effort to keep the salt level in all bread products down to minimum.
"ASDA currently makes a granary loaf with 50 per cent less salt than the equivalent Tesco or Morrisons product," said chairman and professor of cardiovascular medicine Graham MacGregor. "If Asda can keep salt levels down why can't other supermarkets do the same?"
The news is particularly worrying as bread provides a quarter of UK consumers' total daily salt intake, he added.
Small amounts of salt are vital for human health; however over-consumption has been linked to increasing blood pressure, which in turn leads to cardiovascular disease (CVD) and strokes.
As well as urging supermarkets to use less salt in formulation, CASH called for supermarkets to label fresh bread with nutritional information, "as there is no way that customers can tell how much salt is in these unwrapped loaves when they buy them."
Sainsbury's spokesperson Gillian Taylor told BakeryAndSnacks.com that the supermarket has actively campaigned to reduce to levels of salt in its food, and is in the process of re-formulating the recipes for several of its own brand products.
However, she also admitted that the company currently has no plans to use any labeling system on bakery bread products.
Tesco, Morrisons and Waitrose were unable to respond in time for publication.
Under current UK law, only pre-packaged foods must feature nutritional labels listing the ingredients, and detailed nutritional breakdowns are only obligatory when the manufacturer is making health claims, such as 'low fat'.
Fresh bakery bread usually falls outside these categories, so supermarkets are under no legal obligations to label the product.
While pre-packaged bread contains on average 1.5g of salt per 100g of product, slightly more than freshly baked bread, according to Which? statistics, the advantage for consumers is that the exact amounts are always labelled on the packaging.
In the UK, Ireland and the USA, over 80 per cent of salt intake comes from processed food, with 20 per cent of salt intake coming from meat and meat products, and about 35 per cent from cereal and cereal products, according to the UK Food Standards Agency (FSA).
However, campaigns led by both regulatory bodies and advocacy groups have led to the food industry lowering the salt content in many products, including cutting sodium levels in bread by about 25 per cent since the 1980s.
Sodium levels in breakfast cereal have also decreased 38 per cent from 1998 to 2006.