Grab your sunnies, a book and maybe the kids (if that's a thing) and get yourself to one of these hidden gems. London's got a load of green spaces – 47% of the capital is good and grassy – but these are some of the best spots to head to if you're looking to see off your stroll with a healthy amount of snackage.

Hampstead Heath's The Brew House

Kenwood House, Hampstead Lane, NW3 7JR

Maybe you've been strolling the vast grassy expanse of the Heath; maybe you've been splashing around in Highgate Ponds; either way, you should head to The Brew House at Kenwood House for a refuelling sesh, stat. The food's always good, but we'd hold out for the barbecue menu that's served every weekend from 12-4pm on the east terrace over summer. Weather not playing ball? You'll be able to get your chops around a full roast instead.

Dulwich Park's Dulwich Clock Café

College Road, SE21 7BQ

With gorgeous blue hexagonal tiling, wooden beams and temptingly arranged cakes, Dulwich Clock Café is as cute as cafés come. The team makes sourdough pizzas by hand and sources everything it can locally for a menu of Italian-inspired dishes ranging from pasta to salads. It's got plenty of outdoor seating, and makes for an ideal stop-in before, during and after hanging out in Dulwich Park.

Vauxhall Park's Parco Café

190 Fentiman Road, SW8 1QY

Vauxhall Park has sweet lavender gardens, a sweet model village, and a sweet Italian café in its former loos that has a serious food menu. Parco – which looks to Italy for inspiration – dishes up food that more than pulls its weight in the flavour stakes, with housemade lasagne, veal Milanese, calzones and ciabattas. Yum.

Woodberry Wetland's Coal House Café

Woodberry Wetlands, Lordship Road, N16 5HQ

You've got parks, then you've got Woodberry Wetlands: 11 acres of reed-fringed ponds and dykes, close to Manor House and Stoke Newington. Stroll through the nature reserve (entry is free) and refuel at Coal House Café, which serves seasonal food using local producers like Baldwins Butchers and Breid Bakers.

Fowlds Café

3 Addington Square, SE5 7JZ

OK, this one isn't technically in a park, but it is right by the park – and it's so good we're more than happy to make an exception. The space was (and still is) an upholsterer's workshop that was revamped to include a brilliant café serving Square Mile coffee, pastries, cakes, bread and a daily changing season menu. It also runs Fowlds Feasts, a supper club held in the workshop.