Global warming is leading to "profound" population changes in most common fish species in waters off the UK, according to the first "big picture" study of rising sea temperatures.

Around three-quarters of the species affected have grown in numbers, the government-funded study claims.

While cold water-loving species such as cod and haddock fare badly, those that can do well in warmer conditions including hake, dab and red mullet are thriving.

Scientists behind the study of 100m fish hope the research will help governments and environmentalists plan ways of protecting and enhancing stocks.

Marine biologist Steve Simpson, who led the study, said researchers looked at 28 years of data, mostly from fishery agencies, covering more than 1m sq km of the European continental shelf.

Information on the 50 most common species of fish (excluding pelagic fish such as mackerel and herring) was analysed, with 36 judged to have been affected by global warming. Of the 36 species, according to the research, 27 were found to be increasing in numbers.

Simpson, of Bristol University, said: "The bad news for traditional fisheries is that the nine that were in decline were things like cod, haddock, pollack, ling – species of fish that have been a very important component of our fishery.

"Those that were increasing were more exotic species like red mullet, grey gurnard and John Dory.

"We may see a further decline in cold-adapted species, many of which were a staple food for our grandparents. The flipside is a likely increase in species that for the UK seem relatively exotic.

"Over time with effective management and an appropriate response in consumer demand, European seas have the potential to yield productive and sustainable fisheries into the future. There will be more opportunities for fisheries based on species we're not really focusing on at the moment."

The north-east Atlantic has been described as the "cauldron of climate change" with some scientists reporting that over the last 30 years warming has increased at a rate four times the global average. Because waters around the British Isles are shallow and varied, they can be "invaded" more easily.

Simpson said. "We are seeing many more southerly warm-water species faring well on the European shelf. This means more small-bodied faster-growing species with shorter generation times and potentially more diversity."

More work is now being done to try to predict which fish will continue to flourish – or decline.

There was a mixed reaction to the report in Brixham, Devon, one of England's busiest fishing ports. Merchant Nigel Ward, who runs the Brixham Seafish Company, said he believed the seasons that certain species were found in had changed. For example, the lemon sole season used to end in June – now they are still being caught at the end of September.

He welcomed the idea of species like red mullet thriving. "We can find markets for many of these fish. Tastes are changing – people are more willing to experiment."

Rick Smith, managing director of Brixham Trawler Agents, who has more than 35 years experience of fishing at sea, was more sceptical.

Local fishermen had been celebrating a "fantastic" haddock season this year. "I've known it happen twice before – once in the sixties, then again in the seventies. These things come and go," he said.

Smith added they had always caught fish such as red mullet, gurnard and John Dory, though in previous years there was little or no market for much of it.

Fishmongers and restaurant owners say that haddock and cod are still the visitors' favourite fish in Brixham.

"But it is changing," said Dan Brenchley, head chef at the new Simply Fish restaurant. "People are more willing to try fish like mullet, gurnard and dab."

The study was funded by the Department for Environment, Food and Rural affairs and the Natural Environment Research Council and appears in Current Biology.