Robert Brownjohn lived large. Take the weekend he spent in Paris when, flushed with success after designing the opening titles for the James Bond movie From Russia With Love, he stayed at the Ritz and ordered caviar and champagne. The waiter brought him a huge tin of the black stuff. Brownjohn ate and ate till he felt sick, not realising that the waiter weighed the tin at the beginning and again at the end, charging for the amount of caviar he had eaten. Of course, he had unintentionally spent thousands.

Brownjohn, whose work is celebrated in a new Design Museum show, lived like a rock star. His friends included Keith Richards, the radical architect Buckminster Fuller, Charlie Parker, Miles Davis and Michael Caine. He lived and breathed the Kings Road. He partied hard. But his roots were far removed from this high-rolling lifestyle. He was born in Newark, New Jersey, to a bus driver and a housewife. His father, to whom he was close, died when Brownjohn was 12 and very soon “BJ” or “Beej” — as he was known as both to friends and associates — became the black sheep of the family. “They didn’t understand him and he felt like an outsider,” says Eliza, his daughter. “It really affected him. His mother was very strict, icy cold and unemotional.”

Brownjohn won a place at the Chicago Institute of Design, where his mentor was Laszlo Moholy-Nagy, the director of the Institute and Bauhaus émigré. Brownjohn absorbed the pared-down, stark Bauhaus aesthetic. He also got into the jazz scene and, more damagingly, heroin, which became a lifelong addiction. When he married his first wife, Donna, in the mid-1950s, his drug habit was contained. But by 1960, just before he came to England, he had gone off the rails, big style. The designer Ivan Chermeyeff, a close friend, remembers: “If someone says, ‘I’m just going out to get cigarettes, I’ll be back in 15 minutes’, and you spend three days fielding telephone calls from his wife, you know there is something wrong.” Intermittent periods in hospital followed.

Among colleagues in the advertising industry Brownjohn built up a reputation as a maverick; occasionally impossible to understand or be around but a fizzing, inspirational life force for all that. One campaign he created for Yardley featured lipsticks in a gun holster. Another advert, never released, showed a young girl lighting up a cigarette with the voiceover: “Now isn’t it stupid to allow your children to see you smoking”. As Bob Gill, another former colleague, rightly noted: “He was too far ahead of his time.” He was also pretty cocksure about his merits. One colleague remembers him saying to no one in particular: “I’m a f****** genius.”

Sex, and pretty edgy sex for its time, flowed through his work, most famously in a 1963 poster featuring his then-girlfriend Kiki Milne, with “obsession” written in black marker across her breasts (her nipples were the two “O”s). Simple and stark, the picture shows how opposed Brownjohn was to elaborate visual trickery. Emily King, the author of an engaging, substantial book accompanying the show, notes that Brownjohn believed if you couldn’ t evoke images down the phone vividly enough, you might as well not bother committing them to paper.

He designed the famous circular crested Midland Bank logo and distinctive covers for Pepsi World magazine: a shower of Pepsi bottle tops hitting an umbrella, for example. His book covers are brilliantly jolting. Bertrand Russell’s Unpopular Essays features a thumb pointing downwards; Lajos Egri’s The Art of Dramatic Writing features each “i” redrawn as as an exclamation mark. In 1959 he said: “The only real advance in advertising typography has been in the use of type not as an adjunct to an illustration or the image but in its use as the image itself.”

The Bond titles, which will be shown at the Design Museum, make the most of this. From Russia With Love features capital letters projected on to a lithe naked female body, the script rippled by contortions of her body. Brownjohn sold the idea to producers by dancing in front of a beam of light with projected images glancing off his alcohol-swollen belly. “It’ll be just like this, except we’ll use a pretty girl!” he told them.

Nothing was story-boarded. Though the credits look fiendishly complex to do, there was no elaborate planning. “It was all done in the camera, which is the way I like to do films . . . I hate storyboards and scripts. It’s nice just to have an idea and go on the floor and play around with the camera and the lights, and then shoot what you want.”

The sequence was made for £850 and was such a success that Brownjohn raised his fee to £5,000 for the opening credits of Goldfinger, which featured the model Margaret Nolan painted gold and clad in a gold leather bikini, with scenes from the film played out over her body. According to Emily King, Brownjohn took special care with details such as the golf ball that disappears between Nolan’s breasts and the moment when a pocket-sized Bond crawls over her thighs.

Bond producers thought the credits were so good that they offered to finance an independent production studio from which Brownjohn could make future projects. But he turned them down and didn’t do any more Bond credits, clearly not enamoured with the movie production process.

However, nothing Brownjohn did subsequently matched the success of the Bond titles. He designed the wedding cake cover for the Rolling Stones album Let it Bleed, but his reliance on drugs and drink made his behaviour and output increasingly erratic. He moved, alone, into a basement bedsit and died of a heart attack in his sleep on August 1, 1970. The last work he completed was an ambiguous peace poster in which an ace of spades is pasted between the scrawled letters P and E and a question mark. He signed it, “Love-BJ”.

Robert Brownjohn is at the Design Museum, SE1 (0870 8339955), Oct 15-Feb 26. Robert Brownjohn: Sex and Typography by Emily King is published by Laurence King, £25