Widespread direct to household milk delivery in the United States was around long before the postwar suburb, or, heck, even the streetcar Suburb. By the time World War Two was wrapping up milk was a mainstay of the American diet and distributed (alongside butter, cream, cheese, ice-cream, and at times soda) by a swarm of people across the cities, towns and Suburbs of America.
In fact, ironically, it was changes brought about by the postwar suburban lifestyle and prosperity which occasioned it that doomed the widespread practice of home milk delivery.:
After World War II, change came to the milkman. The milkman was a familiar character in the neighborhoods of small towns and cities alike, and dairy products now held an unquestioned place in the American diet. Yet, refrigerators, supermarkets, suburban sprawl, and automobiles threatened home delivery. Consumers chose to live in different places and get milk in different ways. In fact, by the end of the 1950s, home delivery fell into a decline and never recovered. By the early 1950s, reliable power refrigeration replaced ice boxes and revised the homemaker’s job of buying and cooking for the household. Perishable foods like milk could now be bought in greater quantity and kept longer without spoiling, more meals could be made from leftovers, and frozen foods could replace fresh. The milkman did not have to arrive every day in order for the family to have unsoured milk.
If you're interested in Dairy distribution in America in general, with a focus on New England, From Dairy To Dorstep is a neat little exhibition.
Edit: fixed a grammar issue.
For the UK, the vast majority of milk was delivered until relatively recently. This newspaper report gives a figure of 85% for 1980. Section E of this UK government report gives 45% in 1995, 5% in 2010. (I appreciate the latter break the 20-year rule, but these are the only statistics I could find.)
Greetings all. We've had to remove several responses so far. While we understand that many people have personal stories to share about home delivery when they or their parents were younger, this subreddit isn't the appropriate venue: just a reminder that anecdotes are not permitted in this sub.