How lucky we are to have so much open space in London: actually, luck has much less to do with it than a lot of hard work fighting off Victorian property developers and pressing local authorities to maintain parks - but the result is a blessing. Not so long ago, I went on a group walk that started at one of the less attractive stations in south-east London: but someone had cleverly worked out a route that snaked through local parks and woods, and although we were never more than a few hundred yards from main roads and suburban streets, it seemed we were in open country. Passing across one "village green", though, we came across a local kabbadi competition, which you wouldn't expect in Lower Dozing-on-the-Wold.

On a buckshee day off work this week, uncertain weather having encouraged my natural laziness against going for a walk in the country, I simply went out locally instead: there's a clear mile or so through Greenwich Park and across Blackheath.

Avoiding the be-touristed paths up to the Royal Observatory, there's a slightly less kempt path up to One Tree Hill, with its own view, and a verse carved into the seats around the eponymous tree.

Carrying on, there's a rather Victorian flower garden, with some beautiful old trees and lots of island beds, and around the edges rhododendrons in full flower.

Through the high surrounding wall (this was once a palace, after all), you come to Blackheath, a wide open stretch of green with its own vivid history, criss-crossed by some of the busiest main roads in London, but still with plenty of space, not only for people to run around but for more rural touches - a little village pond over by Blackheath villages, and wild flower verges much visited by bees.

More remarkable still, to me, was how chatty people were. I'm not the world's most sociable person, but little incidents (a lost toy perched on the garden railings, a dog stalking a squirrel - clearly without quite knowing why) seemed to spark a series of jokey conversations with complete strangers.

Also in Greenwich Park, of course, is the National Maritime Museum, so I stopped there on the way home. I still think it's a rather bitty collection of seemingly unrelated themes (polar exploration, the Atlantic, how different peoples learnt to navigate, passenger ships, Nelson and Trafalgar, and a hands-on area for children to experiment with all sorts of nautical principles and practice - including, I'm pleased to say, Morse code), but there are plenty of boats, bits of ships and other nautical artefacts to look at and admire. They also have art installations, on this occasion Simon Patterson: he's most well known for his "Great Bear" application of the London tube map to various cultural luminaries, but a lot of what's here passes me by. I liked the sails, though, if only because I love Sterne's Tristram Shandy. They do a nice cream tea, too.

Last stop on the way home was a quick look at the Painted Hall, a celebration of the Glorious Revolution of 1689, the Hanoverian succession and the confounding of Louis XIV. For all the bombast of the decoration, the light of those huge Restoration windows seems very calm and austere.

And best of all, all this is on the doorstep: the trouble with country walks is that it takes such a time to get home afterwards.