When Tina May talks about visiting Scotland as being “like coming home” she means more than the country. The Gloucestershire-born singer has earned an international reputation as the most English of jazz singers, with no mid-Atlantic twang to increase her “jazziness” when she sings and no attempt to hide her upbringing between songs.

May’s late, Glasgow-born engineer father brought the family to visit his roots and kinfolk regularly, instilling a fondness for Cambuslang and East Kilbride in his younger daughter that she maintains by keeping up the links with dad’s surviving siblings in these satellite towns.

It’s possibly also her love of her dad, whom she talks about often, that has drawn May to working with so many Scottish musicians. There’s pianist Brian Kellock, of course, with whom May celebrates the partnership of Ella Fitzgerald and Oscar Peterson on a tour of Scotland this month and with whom she has forged a musical understanding that saw them “rehearse” for, oh, at least 10 minutes before they toured Ella & Oscar to mark Fitzgerald’s centenary in 2017.

Beyond Kellock, though, May has enjoyed similar associations with Duncan Lamont, the Greenock-born saxophonist who worked with Frank Sinatra for twenty years, and once she gets started, she reels off names including saxophonist Tommy Whittle, who beat a similar path to Lamont’s, from Grangemouth to the Benny Goodman band, and the peerless Bobby Wellins, one of Scotland’s great jazz originals, with whom May didn’t record although they did share many stages and conversations about their shared love of Billie Holiday.

Another Scot, and this one’s slightly more unlikely, appears on May’s CV – the impressionist Rory Bremner. May and he were students in Paris when they came up with a revue called – pun haters better look away – You Are Eiffel But I Like You. Wordplay aside, it got May started as a singer. After guesting at Le Slow Club with the Roger Guerin Big Band, which included the drummer’s drummer, Kenny Clarke, who was living in France having worked with Count Basie, Charlie Parker and Miles Davis et al, she formed her first band which included the double bassist’s double bassist, the incredible Renaud Garcia-Fons.

“I could have stopped there and been quite happy, in a way,” says May. “But working with musicians like those makes you want to discover more – more great musicians, more great musical experiences.”

May didn’t grow up expecting to be a singer. She was going to be – indeed she was – a clarinet player and it’s her experience as an instrumentalist that, her accompanists will tell you, makes it easy and such fun to work with her. When she improvises, her inner clarinet player guides her voice.

To watch her onstage these days, with her naturally relaxed air and instantly friendly rapport with an audience, you wouldn’t imagine her being too shy to sing. Cue the tale of May and her similar-aged cousin, Max, trying to hide under the table at a family party in Cambuslang as the party pieces were being trotted out.

“You weren’t allowed to escape,” she says. “My dad’s family weren’t rich – his dad had died when he was 14 and they all had to go out and work – but they’d somehow acquired not one but two pianos. So, singing round the piano was the done thing. It was the same at our house. My mum played piano and we’d sing together. But I remember being terrified of singing in front of everyone at this party. Max got away with it by telling a joke, I think, but I had to come out from under the table and do my song, which was Puff the Magic Dragon, if I’m not mistaken.”

It was at a not-altogether-dissimilar occasion that May first encountered Brian Kellock. The late-night jam sessions at Glasgow Jazz Festival in the 1990s weren’t places for shrinking violets and the singers who were in attendance at the festival were expected to do a song.

May remembers it being slightly intimidating as all sorts of impromptu partnerships were formed by the redoubtable Fionna Duncan, who led these sessions. On one occasion, the big-selling saxophonist Grover Washington Junior dismissed any notions of him being some lightweight, smooth jazzer with a ferociously fluent show of hard-driving, intricate skills. On another, the Scottish saxophonist Laura Macdonald found herself fronting a quartet whose drummer, Dennis Chambers was just off the road with Steely Dan, no less.

“My first impression of Brian at that late-night club was that he was an absolutely brilliant musician,” says May. “That much was obvious but it soon became clear that he was – and is – possibly the easiest-ever person to work with. As an accompanist he’s so generous, so supportive, and because he has every style of jazz you can think of at his fingertips, he’s incredibly responsive. He also has this encyclopaedic knowledge of the jazz repertoire, and it’s so easy so to see why Sheila Jordan, the great doyenne of American singers, adores him. When we talked about playing the Ella & Oscar album, he knew all the songs, asked me my keys and he was right there with me, batting ideas right back at me with his lovely sense of humour and warmth of personality. It’s always a joy to work with him.”

Duncan Lamont, who died last July just hours after playing a gig to mark his 88th birthday and to whom May and Kellock will dedicate their Greenock concert, is held in similar affection by May. Her upcoming album, provisionally titled 52nd Street, brings together a collection of songs that Lamont wrote about characters he encountered, mostly on visits to New York.

“He had this long, long love affair with the city,” says May. “He was of the generation of musicians – Ronnie Scott, Stan Tracey, John Dankworth, all these guys – who, in the 1940s and 50s, worked their passage by playing in bands on the transatlantic liners so they could listen to their heroes in the New York clubs. Duncan was besotted with, not just New York but the culture he encountered there, too, and he captured it in songs. There’s one about a cancan dancer called Camille and another about Fred Astaire and when the bossa nova wave arrived he fell in love with Brazil as well, but 52nd Street, with its jazz clubs, was where he loved to be.”

May and Kellock haven’t recorded together. It’s on her wish list. They don’t even work together with any regularity but every time their paths have crossed over the years, she says, it’s like coming home. On one night of the forthcoming tour, she’ll be working with another Scottish pianist, Euan Stevenson, a generation younger than Kellock but a musician with many of the same musical interests and similar attributes.

“I get the sense,” says May, “that Brian has set a standard, given the younger pianists something to aspire to, even when – as with Euan – they compose their own music as well as playing the songs that Ella and Oscar made famous. It’ll be great to be singing these songs again and especially good to be singing them in Scotland.”

Tina May and Brian Kellock take Ella & Oscar to Beacon Arts Centre, Greenock on Thursday, March 12; Perth Theatre on Saturday, March 14; The Merchants House of Glasgow on Sunday, March 15; and the Blue Lamp, Aberdeen on Thursday, March 19. Tina May and Euan Stevenson play St Peter’s Church, Linlithgow on Friday, March 13.