His restaurants and shops are already so dominant in the Cornish port of Padstow that, to the chagrin of many locals, it has been nicknamed "Padstein".

Now the celebrity chef Rick Stein is planning to extend his foodie empire a little further west and south to Falmouth, until now most famous for its deep natural harbour and proud maritime history.

Stein's company has put in a planning application to build a fish and chip restaurant and takeaway and an oyster bar close to the colourful waterside – all bobbing boats and sweeping views – a move greeted with a mixture of excitement, trepidation and downright grumbling.

Supporters feel that the Stein brand would bring in more visitors and increase spending for other businesses. But some competitors worry that diners will be lost to the TV chef. And more than a few are grumbling that Stein, sometimes seen as an "English newcomer" though he has operated in Cornwall since the 70s, may try to take over the burgeoning foodie scene in Falmouth, as he has in Padstow.

Diana Merrett, a town councillor, said: "What we don't want is this town becoming 'Falstein'. This is an independent, proud town. We wouldn't want one person coming in and changing the feel of the town. I don't understand why he wants to come here and I have my reservations about it."

Though Stein is not talking about his plans yet, they do seem to make good business sense. He may have gone as far as he can in Padstow. In a relatively small town he has four restaurants, The Seafood Restaurant, St Petroc's Bistro, Rick Stein's Cafe and Stein's Fish & Chips. The Stein organisation has 40 guest bedrooms around town, a cookery school, a delicatessen, patisserie and a gift shop. Up the road in St Merryn, it runs a pub.

Falmouth has the potential to become a boom town. Plans are afoot to build a new marina to bring in more yachties and the resort hopes to attract more cruise ships. "Falmouth is on a roll, I can see exactly why he thinks it's a good idea to come here," said Peter Fraser, who would perhaps be Stein's chief competitor.

Fraser owns the Harbour Lights fish and chip shop, a few minutes' walk from the spot where Stein is applying for planning permission. He admits he thought "Oh shit" for "about five minutes" when he heard the news. "But then I thought, well it's great for the town and great to have competition. It's brilliant news."

Fraser reckons Stein's fish may not be to everyone's taste: he batters his fish in beef dripping. "I do mine in vegetable oil. They are two different entities," he said. Price may give Fraser an edge. Fish and chips, mushy peas and a drink sets you back more than £10 at Stein's Padstow chip shop. A takeaway fish and chips from Harbour Lights costs less than a fiver.

Kerry Duffield, the owner of the Seafood Bar, was not sounding so confident. "He's going to do oysters, is he? There probably won't be any point in me doing them then," she said. "It's good for the town but it's going to make life more difficult for the restaurants already here."

Being a celebrity chef in Cornwall is not all plain sailing. Rick Stein and Jamie Oliver, who founded Fifteen Cornwall near Newquay in 2002, stepped up security two years ago after a group calling itself the Cornish National Liberation Army threatened to burn down one of Stein's businesses.

The group also claimed it had Fifteen, set up by Oliver to help disadvantaged Cornish youngsters find a career in catering, in its sights, accusing him of driving up house prices and living costs. Stein and Oliver were offended. Stein's family has had connections with Cornwall for the best part of a century and his businesses have brought in millions to the economy. Oliver's Fifteen is a charitable foundation based at Watergate Bay, a hotel and extreme sports academy that has been operating in Cornwall for five generations. The business is run by local people.

Back in Falmouth, the only evidence so far of Stein's presence is a shelf of his oat biscuits at the Cornish Store, a shop selling all things Cornish. Its owner, Kevin Ayres, said some people could be put off by the Stein name, but added: "I suppose that everything that creates publicity for Falmouth is a good thing."

Customers at Arwenack Fisheries were blunter. "People who go to his places in Padstow and pay those sort of prices are mad," said one local, John. "More money than sense."

Stein's plan has been approved by town councillors and now goes before Cornwall council. A spokeswoman for the chef said: "Nothing has been confirmed as we are in the early stages of planning permission which has now been put forward. I can confirm we are looking at a site in Falmouth and we are in the legal process."

Mike Rangecroft, who organises festivals in Events Square where the new restaurant would be sited, said it was fantastic news. "But I know there are people who think he's ruined Padstow and there are already people here complaining … some people just don't like success."

Billy Fowles, the owner of the All About Olives delicatessen, spoke for many. "It's only a name. I don't suppose he'll be cooking the fish and chips himself, will he? And when it comes down to it, it is just fish and chips, isn't it?"