Young children should be protected from commercial interests, experts told us - while the government said existing laws already set nutritional requirements for baby foods.
A laboratory approved by the United Kingdom Accreditation Service was commissioned by Panorama to independently test the nutritional value of a fruit, yoghurt and savoury pouch from each of the six leading brands.
Our investigation found:
Many of the biggest brands use "halo-marketing" - surrounding products with healthy words or phrases - according to Dr Tedstone.
Ella's Kitchen, for example, describes savoury products as "perfectly balanced for growing babies", while Piccolo claims many pouches are "packed with goodness".
Some Little Freddie pouches come branded as "Good for Brains" and Heinz claims some of its fruit products are "as nutritionally good as homemade".
Piccolo and Little Freddie told us their packaging accurately represented the key ingredients and flavours contained in their products, while Ella's Kitchen said it "would never use" misleading claims. Heinz did not address our questions on marketing.
Savoury pouches are often used by parents as a main meal - but of the six such products sent for laboratory testing, none could provide a significant contribution to the 7.8mg of iron an infant needs in a day.
Iron is a key nutrient for a healthy immune system, growth and brain development - but levels are not shown on the products' labelling.
By seven months old, "babies' iron stores are starting to run out, so we now need to get that from food," explained Bahee Van de Bor, a paediatric dietitian from the British Dietetic Association.
Vitamin C is heat sensitive, which means it degrades because the food inside pouches is heated to ensure safety and increase shelf life.
We tested three separate production batches of the mango pouch, and all came back with the same result.
However, not all the pouches had low results. Heinz's Apple pouch - which has vitamin C added - and Ella's Kitchen's Bananas pouch tested high in vitamin C.
Piccolo said vitamins degrade during processing, so it boosts many of its fruit pouches with ingredients rich in vitamin C. Ella's Kitchen said it keeps the loss of vitamin C to a minimum.
None of the other brands commented directly on our vitamin C results.
We also found that the six companies had failed to implement some NHS, Public Health England and WHO recommendations.
Piccolo, Aldi and Ella's Kitchen currently promote their fruit pouches to babies as young as four months, despite the NHS and WHO saying babies should not be given solid food until about the age of six months.
Introducing products at four months old, added Dr Tedstone, is "a whole eight weeks of extra product sales".
"I think we should put our babies' health ahead of commercial incentives to sell more product," she said.