Chat with Skye Gyngell for two minutes and it's easy to understand why the Australian-born, Paris-trained chef has called London home for more than 30 years.

Gyngell, who shot to celebrity chef-dom in 2011 when Petersham Nurseries Cafe was awarded a Michelin star under her guidance, speaks of a London rich with farmers' markets, wine bars, artisan cheese and Eccles cakes worth crossing boroughs for. A city of gardens and swimming ponds, and parks in which to crack a rosé for a spell in the sun. (Just as long you don't visit between January and March, when it's "cold, damp and dark", she says.)

The Sydney-raised chef now helms Spring restaurant at Somerset House in central London, a must-visit for elegant, produce-driven cooking – stracciatella with crushed peas, white asparagus and lemon verbena, say, or wild sea bass with borlotti beans, slow-cooked zucchini and salsa verde.

Once you have ticked a Spring lunch off your list, Gyngell has myriad other suggestions for getting the most out of Old Blighty's beating heart.

To market to buy a fat pig and cheese

Well, maybe not a whole pig, but certainly a pork pie or sausage roll from the Ginger Pig, a chain of gourmet butchers with shops dotted around London, including Marylebone. "Their traditional pork pies are incredible," Gyngell says. "Next door to Ginger Pig is La Fromagerie with a beautiful walk-in cheese room, and you also have Marylebone Farmers Market every Sunday, which is really lovely."

Gyngell lives in west London, but says her absolute favourite market to visit is Spa Terminus on the other side of town at Dockley Road Industrial Estate. "It was started by Randolph Hodgson of Neal's Yard Dairy, who took over all these archways at a defunct railway station," she says. "There's a Neal's Yard stall for British farmhouse cheese, plus Mons Cheesemongers, where a guy named John brings in the most beautiful French and Swiss fromage. Aubert and Mascoli is an amazing natural wine merchant there, and you should also track down Kitty Travers at La Grotta Ices. Kitty was a St John chef for a long time and her ice-creams are brilliant."

Seasonal Grotta specialties include a tangy-tart prosecco and grape sorbet, and raspberry and fig leaf gelato.

Push the boat out on the river

"One of the most expensive meals you're going to have in London, but also one of the best, is the River Cafe," says Gyngell of the Hammersmith Italian restaurant opened by chefs Ruth Rogers and Rose Gray in 1987. "To sit outside on the weekend for lunch, when the weather's lovely and there's kids rolling around on the grass, there's nowhere nicer in London. And if you're thinking River Cafe is fancy pants, it's not – it's quite unpretentious. It just has very fancy pants prices."

Gyngell is also a big fan of 40 Maltby Street, an understated natural wine bar where you might enjoy radishes with goat's curd and brown butter, or grilled lamb's heart enhanced by anchovy, cucumber and mint. "It's the nicest wine bar in London and loved by all the chefs I know," she says. "Cocktails are also really big in London right now. Everybody is talking about the drinks at Bar Termini, a tiny little hole-in-the-wall in Soho."

The chef also recommends snacks at wine bar Noble Rot, wood-fire grilled seafood at Brat, tapas at Sabor and lunch at Lyle's. "James Lowe [at Lyle's] is a very intelligent, thoughtful chef," she says. "A lot of people say the room is too small and the music is too loud for a Michelin-starred restaurant but I really like the space."

Picnic in the park

London has more than 1700 parks, commons, public gardens, and converted churchyards to roll the rug out for lunch.

"If you want a wild and beautiful space, Hampstead Heath is a real thing to do with ponds complete with old-fashioned diving boards," Gyngell says. "It's just divine to pack a picnic and go for a swim. Melrose and Morgan is nearby and provides great food for the occasion – very Ottolenghi. Lots of salads and sandwiches and house-made jams."

Kensington Gardens is also prime for picnicking, Gyngell says. "All of Notting Hill is at your disposal for supplies there. Sally Clarke has been around forever on Campden Street and does very English food – chicken and mushroom pies, for example, smoked salmon and watercress sandwiches, and the most wonderful Eccles cakes. Make sure to visit Serpentine Gallery in the Gardens, too."

Details

The Ginger Pig, thegingerpig.co.uk

La Fromagerie, lafromagerie.co.uk

Marylebone Farmers Market, lfm.org.uk/markets/marylebone

Spa Terminus, spa-terminus.co.uk

Neal's Yard Dairy, nealsyarddairy.co.uk

Mons Cheesemongers, mons-cheese.co.uk

Aubert and Mascoli, Arch 2 Voyager 4RP, Spa Road, Bermondsey

La Grotta Ices, Bermondsey Spa Unit 12 (between Spa & Dockley Road), Bermondsey

​The River Cafe, rivercafe.co.uk

40 Maltby Street, 40maltbystreet.com

Bar Termini, bar-termini.com

Noble Rot, noblerot.co.uk

Brat, bratrestaurant.com

Sabor, saborrestaurants.co.uk

Lyle's, lyleslondon.com

Melrose and Morgan, melroseandmorgan.com

Sally Clarke, sallyclarke.com/restaurant

Skye Gyngell's baked eggplant salad with tarragon and creme fraiche is available to order now until Friday, June 21, in Sydney and Melbourne through twogood.com.au. For every meal sold through food charity Two Good, another is donated to a domestic violence shelter or refuge.