There is still too much salt in processed meats such as sausages and bacon and ready meals, a Public Health England report suggests.
The groups of foods were among those that met none of the average salt targets set by PHE in 2014.
But some other foods, including breakfast cereals, baked beans and pizzas, did meet the voluntary targets.
The meat industry insisted it was "playing its part" in reducing salt in its products.
Too much salt can raise your blood pressure, which puts you at increased risk of heart disease and stroke.
Most of the salt we eat is already in everyday foods, rather than added at the table.
Retailers, manufacturers and restaurants, cafes and pub chains were all asked to meet average and maximum levels of salt per 100g (3.5oz) by 2017 across 28 food categories.
- Meat products – which include items that have been processed with salt but not things such as chicken breast or steak – met none of the average targets and 43% of items contained more than the maximum salt levels
- Ready meals, soups, biscuits, rice, other cereals and meat alternatives, such as veggie burgers and sausages, also did not meet any of the average targets
- Breakfast cereals, fat spreads, baked beans, pizzas, cakes, pastries, fruit pies and other pastry-based desserts, pasta, quiche, processed potato products, stocks and gravies did meet the average targets
Across all categories, average salt level targets were met for about half of foods consumed in the home in 2017.
PHE said "clear progress" had been made since work began to reduce salt intakes in 2004 but that further "realistic but ambitious goals" were needed.
Dr Alison Tedstone, chief nutritionist at PHE, said: "While we have seen some progress, those that have taken little or no action cannot be excused for their inactivity.
"It is clear that, with the right leadership from industry, further salt reduction in foods continues to be possible."
What are the recommended daily maximum salt consumption limits?
The foods covered by the targets are the main contributors to dietary salt intakes in adults in the UK and provide about 54% of salt in the diet.
Overall, 81% of products consumed in the home had sodium levels at or below their maximum target level.
For food eaten out of the home, 71% of products were below maximum target levels.
According to the most recent data available, adults in England consume about 8g per day of salt – nearly a gram less than in 2005-06.
PHE estimates that bringing that figure down to 6g a day could help to prevent thousands of avoidable deaths.
Prof Graham MacGregor, who chairs the campaign group Action on Salt, criticised the level of salt reduction achieved.
He said: "Such poor progress in PHE's attempt to reduce salt intake is a national tragedy.
"This report confirms what we know already – that voluntary targets need comprehensive monitoring and guidance but this has been completely lacking from PHE."
Public Health England expects to publish an assessment of current salt intakes for adults in England by early 2020.
Consumers can check how much salt is in different products by looking at the nutritional values displayed on the packaging.
Some products also carry "traffic light" colour-coded displays, with red indicating something is high in salt.