When a famous person snaps up a local business the expected response might, at best, be a shrug and, at worst, outright hostility. But not so for Norman Cook aka Fatboy Slim, who in June opened the Big Beach Cafe at Hove Lagoon, an easy 20-minute cycle from the centre of Brighton along the seafront.

Tucked just below the beachfront, it sits in the shadow of a new skate park and kids' playground with paddling pool. Cook can practically see his house from the cafe. "I've lived on the beach for 15 years and brought both my children up in this park," he says. "I've had some very happy years here. It sounds a bit cheesy to say I want to give something back but I want to cement my relationship with the community and get really into the heart of it."

The gist of local response seems to be: "great news, good luck to him". This may be because the cafe was previously owned by Heather Mills, who perhaps doesn't have the biggest fan base in the world. It was also vegan and some customers resented not being able to get a regular milky coffee or non-soya ice-cream for miles around. But more likely it's because Cook is a popular guy in Brighton and Hove. He went to college here, has a stake in the local football team and, with his Big Beach Boutique concerts, has hosted some of the biggest parties the area has ever seen.

This is not his first foray into food. A decade ago a friend warned him that "the music business was getting a bit stale" and that he should open a restaurant. He now has "interests" in three other restaurants. Two are in New York and include The Spotted Pig, a Michelin-starred gastro pub which is also backed by Jay-Z and Bono. Oki-Nami is his Japanese restaurant in Brighton. "It's a sideline that I've gotten into as I get older and wiser and calm down a bit; it made sense to carry on doing it ever closer to home," he says.

I ask why he wasn't tempted to set up something more swanky? "There's never really been a high-end restaurant that's succeeded in Brighton, the kind of people who want high-end food go up to London for it. Brighton is much more about cafe society."

Aside from the cool signs painted by local graffiti artist Aroe, it looks conventional from the outside and a little weather-battered, as seaside cafes tend to be. Inside it's light and airy, with an open kitchen and stylish curved wooden counter. The art is lifted from Cook and his wife Zoe Ball's collection. He says: "Zoe's is the film stuff and mine is the surfy stuff with a slight tie-in to the Big Beach parties. I didn't want to over-egg that side of things though. We're not going to do a Rockafella burger or Santa Cruz fries or anything like that."

They're presently serving a mix of classics, such as burgers and ice-cream, alongside scotch eggs, veggie tarts, pies and cake, using local, independent suppliers where possible. The coffee is from Small Batch, a nearby roastery, and the burgers made with baps from a local baker. Gourmet burgers? I suggest to Danny Stockland, the head chef. "Semi gourmet," he says. "You'd pay £13 for a gourmet burger in Brighton but we're serving them for £4.50," he says. "Having it reasonably priced is very important to us. I'm a father with two kids, if I was being priced out the market I'd just turn up here with a picnic."

I had the spinach, feta and tomato quiche, my son had a sausage roll and a smiley face cookie, while my partner went for the full-on fry-up. They also do super-tasty cakes that shouldn't work but do, like courgette and lime cake, and beetroot and chocolate.

The cafe-bar is now open 10am-6pm; they recently hosted Norman's 50th. They have a rainproof marquee space outside and the plan is to open in the evening soon, serving steak-frites and fresh-off-the-boat fish. I ask Cook about the music. "I'll be providing it and it'll be 100% Fatboy Slim free!"

The cafe's picnic tables face Hove Lagoon, which isn't the tropical body of water its name suggests but a fun watersports hub nonetheless. A path across its middle can give the pleasing illusion you're watching skateboarders glide on water, and the cranes and chimney at Shoreham harbour add a post-industrial backdrop. Traditionally a windsurfing and sailing spot, it's now just as popular for SUP (stand-up paddling), as it's quick to pick up, and wakeboarding. It's also sheltered, so especially good for kids and beginners.

It's not hard to see why Cook loves it here: "If you're in a big city you feel hemmed in by the noise and nonsense and pressures going on all around you. But here, whatever shit goes on, you can always escape and look at the sea."

• Big Beach Cafe, Hove Lagoon, 01273 911080, bigbeachcafe.com