A third of breads contain more salt than recommended under guidelines being introduced next year, a survey found.
Most breads were within the current guidelines of 1.1g of salt per 100g - but this is being cut to 1g per 100g.
Campaign for Action on Salt and Health (Cash), which looked at 300 breads, said it was "outrageous" that bread contained even the current level.
The Department of Health said "considerable" salt reductions had already been made.
Manufacturers said many loaves with the lowest salt levels were supermarket brands, which were the most popular.
Eating too much salt is linked to high blood pressure, which in turn increases the risk of developing heart disease.
Recommended dietary salt levels vary with age. Adults are meant to have no more than 6g of salt in their diet per day, while toddlers should have no more than 2g.
Salt levels in bread have fallen by about a third over the past decade, with some falling by up to 40%.
But Cash says levels are still too high, and warns there is wide variation in the amount found in loaves.
Most are within half a gram of the current target of 1.1g of salt per 100g of bread - about two thick slices. But Cash found some significantly exceeded it.
Cash says consumers should look at nutrition labels, where possible, to see how much salt bread contains.
But it warns fresh breads, from in-store or high-street bakeries have no nutritional labelling, meaning people cannot tell how much salt they contain.
And it said bakery breads often had higher levels than their packaged products.
Cash chairman Prof Graham MacGregor, of the Wolfson Institute of Preventative Medicine, said: "It is frankly outrageous that bread still contains so much salt.
"The Department of Health needs to ensure that all bread is clearly labelled and that all manufacturers reduce the salt of bread to less that the salt target of 1g per 100g.
"It is the very high levels of salt that is hidden in everyday food, such as bread, that puts up both adults' and children's blood pressure."
Victoria Taylor, senior dietician at the British Heart Foundation, said: "We know too many people are eating too much salt each day. Some manufacturers are working towards targets for salt reduction, but we need more action to cut the salt content in bread and make sure they provide colour-coded food labels to help their customers."
But Federation of Bakers director Gordon Polson said: "The majority of wrapped, sliced bread available already meets the 2012 targets and our members are continuing to endeavour to reduce salt by contributing to ongoing research to establish which other means are available to reduce salt in bread.
"The vast majority of breads singled out in the Cash report as higher in salt are not the mainstream products produced by our members; which do produce around 80% of the nation's bread in a £3bn industry."
A Department of Health spokesman said the government welcomed the "considerable" salt reductions that bread makers had already made, and it was "very pleasing" that around 60% of the products met salt targets for 2012.
"This is an important step in helping to reduce salt intake, as well as lowering the risk of high blood pressure and resulting strokes and heart disease. We look forward to seeing further reductions as more companies meet the targets," he added.
British Retail Consortium food director Andrew Opie said retailers and manufacturers are to fund independent research to look for ways of meeting the 2012 target - "while still making foods which consumers want to buy".