The premise of my three-part series Hugh's Fish Fight (shown on Channel 4) is to highlight that the fish-eating habits of this nation are seriously misaligned with the long-term viability of our fisheries. More than half the fish we eat comes from just three species – cod, tuna and salmon. You don't have to think too hard about that statistic to see the problem.

The first two shows focused on cod and tuna. Cod, a fish we have all been told is in big trouble, is being thrown back dead into the North Sea in vast quantities because of crazy EU quota rules. There has already been a very strong reaction to the anti-discards campaign Fish Fight. Thousands have signed up to our protest letter to Brussels, Defra (the Department for Environment, Food and Rural Affairs) has launched a new initiative to try to reduce discards, which includes finding new markets for "neglected" species, and fisheries minister Richard Benyon has pledged to put the issue "at the top of the agenda for CFP (the EU's Common Fisheries Policy) reform".

This evening you will see me challenge Tesco and Princes over their tinned tuna, which their suppliers catch by purse seining, where massive fishing boats with 2km-long nets lasso whole shoals of tuna. They also use controversial fish aggregation devices (Fads), which are floating rafts anchored to the sea floor designed to attract shoaling fish. Fads are highly effective at enticing tuna shoals for the purse seiners to surround with their nets, but they also dramatically increase the bycatch of the "wrong" species – including turtles, sharks and rays.

On Monday, Greenpeace published its assessment of the supermarkets' ecological rating for tuna. Tesco was due to come last on the list, but anticipating our shows and the Greenpeace findings, it announced at the weekend that it would be switching its entire own-brand tuna to the far more sustainable pole and line method of fishing. It leaves Princes stranded bottom of the league table – but the company has at least indicated it will withdraw from its tins the claim – outrageous, in my view – that Princes is "fully committed to fishing methods that protect the marine environment and marine life".

The last show also looks at the third problem fish – farmed salmon. I visited Marine Harvest on the west coast of Scotland, the biggest salmon producer in the world – it also has farms in North and South America and Scandinavia – to challenge it on the fundamental problem underlying the business of farming this carnivorous species: that it takes more than three kilos of wild fish to produce the feed for just one kilo of farmed salmon. Marine Harvest says it is working to reduce its reliance on wild feed, and to ensure that the feed it uses comes from sustainable stocks. But, right now, not one of its Scottish farms is using a feed certified as sustainable by any independent auditing body.

Incidentally, I singled out Marine Harvest simply because it is the largest – and therefore has the biggest impact on the environment. The same feed issues apply to most of its competitors. The exception is the organic sector. The feed for organic salmon comes not from wild fish, but from the "offcuts and trimmings" of the fish-processing industry – fish that was already destined for the human food chain. This makes a lot of sense and, for those who like to eat farmed salmon, switching to organic can only help to grow this more sustainable end of the business. Currently, it represents less than 5% of the market, and consequently you will struggle to find it in most supermarkets – Waitrose and Sainsbury's take the lion's share.

My visit to one of Europe's largest salmon feed producers, Scretting, near Inverness, revealed some other interesting aspects of the salmon problem. In their lab, I was amazed to see a colour chart for salmon flesh. Supermarkets order the colour they think their customers will like best (how could they know?), and the feeds are adjusted accordingly, using a food dye called astaxanthin. Originally, the idea was to mimic the natural pinky-orange of wild salmon flesh that comes from a diet rich in marine crustacea. Without the chemical pigment, the flesh of farmed salmon would be a drab grey. Now the colour of farmed salmon flesh is decided by the marketing teams of the big retailers.

Scretting also told me that it is now possible to produce a feed for salmon that has no fish in it at all. But UK supermarkets are not keen, as it means drastically reducing the omega 3 levels in the finished salmon – and these healthy fish oils are a key marketing point. So the next technological fix, Scretting revealed, is to put the omega-3 back into the feed by splicing the genes of marine algae with a rape-seed crop. The resulting genetically modified feed would be given to the salmon, which might also be genetically modified to thrive and grow at accelerated rates on such a feed. But in a world where, properly managed, the oceans could supply us with sensible amounts of truly wild, and natural, omega-rich fish flesh – do we really need to create something like this?

Pelagic oily species such as sardines, anchovies, herring and mackerel – which are being industrially abused to feed pigs and chickens as well as salmon – should be better managed, better processed and better marketed to us. Instead of feeding these to salmon, why aren't we eating them ourselves? They happen to be four of my favourite fish – delicious and full of omega-3 oil. Yet people are put off buying them. The problem for many seems to be small bones yet, in the case of sardines, mackerel and herring, the supermarkets already have the technology to present these fish in neat, completely boneless fillets that are just as easy to cook and eat as a chunk of farmed salmon.

Others claim to find these fish a bit too "fishy", and it's true that pan-frying sardines in your kitchen can create quite an atmosphere. So bake them in the oven (sprinkled with some finely chopped herbs and garlic); problem solved. I think it is time for supermarkets to put some of the energy, marketing clout and recipe know-how that currently goes into shifting vast amounts of farmed salmon behind these more sustainable species.

I am not calling for a mass boycott of farmed salmon. But I am challenging the industry to demonstrate that it can be sustainable in the coming years. Powerful companies such as Marine Harvest should grow the organic side of their salmon business and invest in farming more sustainable, herbivorous species, such as tilapia, carp and pangasius (catfish). And I am asking consumers to consider the wisdom of making salmon their one and only fish choice – as many apparently do. We need to embrace variety in our seafood, to be more adventurous in our fish cooking. There are some cultural barriers to cross in getting to grips with unfamiliar species such as dabs and flounder, gurnard and black bream, coley and pouting. But crossing them should hardly be a chore, for any one who is genuinely enthusiastic about eating fish. And cross them we must – fishermen, wholesalers, retailers and shoppers – if we want our children to eat fish. By spreading our nets wider, but less deeply, we can lighten the load across the world's oceans, for generations to come.

Hugh's Fish Fight is on Channel 4 on 13 January at 9pm. To sign up to the campaign, visit fishfight.net