In other words London capitalises a lot on existing fabric, laid down by the original rail lines that led to the suburbia. It's pure luck a lot of this housing went up before the rise of the automobile, and London's biggest building boom was in the 1930s, just before auto use became full-blown. Although a lot of roadage was laid out, everywhere was still connected up by rail and tube.
New Towns that dot the country, that went up postwar and didn't enjoy the historical luck suffer the exact same suburban monoculture as the States. Property rights are paramount, and until last year nimbys had the ball, easily (nowadays new developments can slip under the radar just by using posters as consultation, rather than door to door leafleting).
Milton Keynes is notorious -its centre is a series of shopping malls
https://c8.alamy.com/comp/f3ft03/an-...-uk-f3ft03.jpg
However even here things can change. Where they do have to build in the midst of the suburban housing -den of snakes that it is -they get around by burying unused roads and building on verges. Of existing homes nearby it's easier to build in the midst of apartment dwellers who already live with the density, and renters who don't care. Everything surrounding the devlopments below were apartment blocks (though from the air they look like SFHs).
and you get positively urban
www.movingcity.co.uk
In effect it goes from this (1930s):
to this (1980s), raising the height subtly, stocking renters, apartment dwellers and businesses while keeping to the suburban vernacular
A decade or two later up the ante, and maybe the odd tower, in the right places.
and at the end you start building dense urbanity, slipped under the noses of the nimbys
www.dutchanddutch.com
Also any tube/ railway/ bus stations sit on a large amount of dead land, used up in verges, approaches and car parks. Building on these areas often start the inroads to developing the wider area as more people move in for the convenience to the network, and demand more urbanity and shops.
In short, build in the ugly spots -car parks, verges, factory yards, warehouses, 1980s business parks. Site them near existing shops and public buildings that dot suburbia (eg schools, gyms, suburban offices), and renters. Never touch a golf course, church or park.