In East Dulwich, there is more charm, with a Saturday market on North Cross Road, Edwardian rowhouses and a slightly spooky brick Victorian hospital, still in use. Gentrification has brought a busy high street filled with gastro pubs, cafes, hair salons, boutiques and a good French bistro. It was a far cry from my memories of Lewisham High Street, where more than three decades earlier I’d go shopping in mainly shabby stores for things like shampoo and dental floss, returning to my dreary dorm in time for the bell summoning us to tea.

Speaking of gentrification, there’s a reason London is so expensive: Everyone wants to live there. Which is why all kinds of formerly drab neighborhoods are hot. Abbey Wood, 10 miles east of Charing Cross, is not, however, one of them, though if you like ruins (I do), there’s a fine one to be had at the ancient Lesnes Abbey, founded in the 12th century, and today surrounded by parkland and footpaths.

But for real urban rehab, Clapham is more like it. Clapham has an upper-class background (Samuel Pepys enjoyed a countryside lifestyle here at the end of his life). However, after the railways came in the 19th century, Clapham became accessible to commuters and hence developed as a suburb, becoming synonymous with the ordinary, if reasonable, citizen. (Hence the term, introduced into English law during the reign of Queen Victoria, “man on the Clapham omnibus,” to indicate what the man on the street would do in a given circumstance.) Enter young mothers who want more than a single-room flat in which to raise their young, and voilà: the huge green expanse of Clapham Common, ringed with mansions and filled with tennis players, runners, dog-walkers and a zillion moms pushing a zillion babies — giving rise to the nickname “Nappy Valley.”

In the area’s physical valley, on Northcote Road in Battersea, I came across a veritable traffic jam of prams, along with design shops, coffee emporiums and my own destination: the Northcote Road Antiques Market, with some 30 dealers under one roof, and enough bric-a-brac, crystal, vintage fabric, Art Deco knick-knackery, flatware, pictures, prints and furniture to outfit a small country in good, if fanciful, taste.

If you like markets, nothing beats the one in Brixton, consisting of open-air shops along Electric Avenue and covered markets. There’s nothing that can’t be found there, including wigs, jewelry, electrical gadgets, secondhand CDs, and just about every kind of fruit and vegetable and fish.

When people in the warmer reaches of the British Empire started immigrating to London in the 1940s and ’50s, it was largely to Brixton that they moved, and today Brixton includes a mix of African and Afro-Caribbean residents, accents and, most importantly, cuisines. I had one of the most memorable — and inexpensive — meals of my adult life at a blink-and-you-miss-it kiosk called Bushman Kitchen on Brixton Station Road, where there was no menu, and the man who served me insisted on making me something special, which I couldn’t get in America, and produced a jerk chicken roti with plantains and cabbage that was so delicious I wanted to move to Jamaica.