You know a company is doing something right if it can keep a notoriously picky customer happy down the years.

So it was with Turnbull & Asser and Frank Sinatra. Ol’ Blue Eyes was famously particular about his clothes. This was a man with rules – no brown after dark, no tuxedos on Sundays, pocket-handkerchiefs to be orange. ‘Yes, he had very precise tastes,’ says head cutter David Gale, ‘which is why he came to Turnbull & Asser. For instance, just like Ronald Reagan, he preferred a particular collar style, which sits very low down on the neck. He must have liked what we did, because he stayed with us – there were no second chances with Mr Sinatra, as some other shirt makers can attest.’

We also discuss another aspect of Sinatra’s sartorial preferences – that Frank liked some of his bespoke shirts to button under the crotch. ‘It’s called a Quorn strap, like the hunt, and it runs from the tail and is attached to a lower button at the front. It was originally designed for hunting, so the shirt didn’t pop out of the breeches, but in his case it would be so he could lift his arms on stage without the shirt bunching or coming adrift.’

Where the taste-making Chairman of the Board went, others were bound to follow and Ratpacker Sammy Davis Jr also became a Turnbull & Asser aficionado (at least, until he got into kaftans and Nehru collars during his hippy phase), as did fellow crooner Tony Bennett. ‘We have made Mr Bennett many shirts over the years,’ says Gale, ‘and he still pops into the shop whenever he's in town, usually to buy ties or cufflinks or other accessories.’

The Beatles were also customers – for pyjamas. ‘Yes, we made silk pyjamas for them, but not as a matching set – they liked to customise them. Ringo might have epaulets on his, Paul had pointy collars, John two pockets. George’s was probably the most traditional of the lot. Paul McCartney and Ringo Starr also had shirts made by us.’

Most musicians, like regular customers, come to Turnbull & Asser for their bespoke shirts because, as David Gale says, ‘They fit incredibly well, thanks to the number of measurements we take - usually 15 to 20 - can be in any style and fabric, and last for years.’ So the likes of Mick Fleetwood, Art Garfunkel and even Liberace were simply shopping for beautifully tailored off-stage clothes. But some musicians are drawn to the St James’s shop because they have performing requirements. ‘Pianists, by which I mean concert pianists, require more room in the back of the shirt for the reach, and also need shorter cuffs than we usually offer, because they don’t want anything coming near the keyboard as they play.’

Jazz pianists – such as Oscar Peterson and Harry Connick Jr, both Turnbull & Asser clients - don’t have such stringent requirements. ‘The jazz world is not as intensely formal as the classical one, nobody stresses over a stray cuff, so a regular shirt is fine.’

One exception is André Previn who, although possibly best known to the wider public these days for a certain TV comedy sketch, has formidable jazz chops as well as being able to play all the right notes in the right order in the classical repertoire. He had his Turnbull & Asser shirts made with the extra volume in the back and the shorter cuffs, so he could switch effortlessly between the two worlds.

Another jazz icon, Miles Davis, who, in the Fifties and early Sixties, was the epitome of well-tailored cool, was a customer, but not at Jermyn Street. ‘He had his made in the days when we shirtmakers travelled to New York to measure clients,’ said Gale. ‘Mind you, they had to be patient – it took up to six months before delivery back then.’ These days, even though the shirt-building process has changed very little since Miles’s time, delivery is four to six weeks, not months. Still, a Turnbull & Asser shirt is always worth the wait – as he used to growl: 'For me, music and life are all about style.' Sinatra himself couldn’t have put it better.