The noun Sloane Ranger denotes an upper-class and fashionable, but conventional, young woman in London.
—Masculine equivalent: Hooray Henry.

The noun Sloane Ranger is a blend of:
– Sloane Square, the name of a square located in an affluent area of London;
– Lone Ranger, the name of a well-known hero of western stories and films.

The noun Sloane Ranger is said to have been coined by the British cultural commentator, management consultant, author and broadcaster Peter York (Peter Wallis – born 1944) in an article published in Harpers & Queen (London, England) of October 1975.

The following explanations and drawing are from the Daily Mirror (London, England) of Tuesday 4^th May 1976:

The all-girl tribes that menace every male . .
Man-hunters on the march
by Jill Evans

It’s not so long since Maurice Chevalier ¹ was publicly thanking heaven for little girls.
Poor Maurice . . . you have to wonder whether he’d be quite so grateful today.
Perhaps we live in harder, less-romantic, times, but those “little girls who grow up in the most delightful way” have certainly changed quite a bit.
The name of the game now is tribes . . . all-girl tribes, sharing life-styles and chalking war-paths right across the country.
The posher parts of London have two tribal groups—the Sloane Rangers and the Mayfair Mercs (short for mercenaries).
The names were coined by their own manual, the glossy Harpers and Queen magazine.
The Sloane Rangers are good stock, usually answering to the name Caroline.
Their spiritual homes are Chelsea’s Sloane Square and Harrods, and they wear head-scarves, even when they haven’t got their hair in curlers.
They’re little replicas of Princess Anne. Pedigree.
The Mayfair Mercs are predators, soldiers of fortune whose prey is what belongs to the Rangers—husbands, boyfriends, brothers (as long as the inheritance has held out long enough for sleek cars and well-stacked wallets).
Their hair colour (blonde, like gentlemen prefer it), accents (sophisticated drawl) and names (Mikki, Vivian, Sam) are picked up along the way.

¹ Maurice Chevalier (1888-1972) was a French singer and actor.

Drawing by Glyn Rees, illustrating Man-hunters on the march, published in the Daily Mirror (London, England) of Tuesday 4^th May 1976:

SLOANE RANGER:
good stock

The earliest occurrences of the noun Sloane Ranger that I have found are as follows, in chronological order:

1-: From Londoner’s Diary, published in the Evening Standard (London, England) of Wednesday 1^st October 1975:

This morning a posse of photographers awaited Miss Kennedy’s arrival. A few Sloane Ranger types (Gucci shoes, Hermes scarves, velvet jackets and navy blue tights) wandered in and out, but the word came that she would not turn up until the afternoon.

2-: From the Daily Mirror (London, England) of Monday 29^th December 1975—in order to mark the coming into effect of the Equal Pay Bill and of the Anti-Discrimination Bill, several of the Daily Mirror’s women journalists “spelled out the situations which made them mad in 1975”:

Chauvinists are worse
It’s not so much discrimination I object to as chauvinism, writes Mary Griffiths.
For instance, the doorman at THE top hotel who stopped me going in for afternoon tea—because I was an unaccompanied woman.
Or the under-manager of a big hotel off Sloane Street, who agreed that the mixed party of titled Sloane Rangers in the bar were behaving disgustingly, but then asked US, my woman friend and me, to move to the upstairs bar.
Finally, the numerous taxi-drivers who by-pass my hail—and go straight for a man.
If they think they’ll get a bigger tip they’re wrong. I make a point of paying big tips to taxi-drivers.
I like the feeling of superiority it gives me—over a mere male driver.

3-: From Londoner’s Diary, published in the Evening Standard (London, England) of Wednesday 31^st December 1975:

There is a chance that the fashion conscious will discover individuality. Grace Coddington ² told me that she hopes people will use more imagination putting clothes together. “I don’t like the total look,” she explained. “The best dressers are immensely individual.”
Comment which is hardly going to please the Sloane Rangers, the hardy breed of girls so neatly described in the Harpers-Queen’s catchphrase. They’re looking forward to a boom year with among other things tee shirts bearing the legend on offer from Lady Charles Spencer Churchill.
It’s a phrase which may helpfully circumscribe the lunatic fringe who are already cantering off for the first few run-ins under the Sex Discrimination Act. Already an ad has appeared in The Times saying “Sloane Ranger seeks flat with cheers. . . .”

² Grace Coddington (born 1941) is a Welsh former model and fashion editor.

4-: From King’s Road, where are you now?, by Suzy Menkes, published in the Evening Standard (London, England) of Monday 5^th January 1976:

The King’s Road today is back in business serving its locals, the silk headscarved Sloane Rangers of Belgravia, with a place in the country and an account at Peter Jones.

5-: From the television programmes published in the Evening Standard (London, England) of Friday 9^th January 1976:

ITV
[…]
6.0 LYNDALL’S LONDON GIRLS. Lyndall Hobbs reports on the Sloane Rangers—the girls who, according to an extremely witty friend of mine, chuck babies under the chin while gurgling “Gucci-Gucci-Gucci.”