She has seven No 1s but Jess Glynne tells Neil McCormick she's not feeling the usual pop pressures.

The first time Jess Glynne heard she was No 1, she wanted to throw up. "That was the biggest shock of my life," the 28-year-old pop singer-songwriter gushes. "I'd got some weird bug and I was really ill. Radio 1 called, and I was on air, in tears, all the time trying not to be violently sick. I was like 'That's amazing! Bleaurgh!"'

Glynne has had seven UK No 1 singles, more than any other British solo female artist. More than Kate Bush, Sade and Annie Lennox. And more than her heroes Amy Winehouse and Adele - and this despite having only released one album so far.

"It's mad, weird, it's hard to get your head around," she declares in a rushing torrent that is her de facto style of conversation. "I don't even feel that famous."

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When she gets recognised on the street, she sometimes denies it's her. "I'll be walking and a voice goes, 'Oh my god, are you her?' I just say 'No, it's the hair'," she laughs.

Glynne has a long red mane, which she fiddles with as she talks, sweeping it back from her face. "I've never felt I look like a pop star," she admits, then immediately questions that. "What is a pop star supposed to look like?"

Chances are you would recognise Glynne's voice, even if you did not recognise her. It has a fierce and direct quality, a round tone with just an edge of hoarseness and distinctive vibrato. It was the voice of dance music outfit Clean Bandit's inescapable 2014 single Rather Be.

Its success made her an in-demand collaborator on chart-topping hits with Rudimental, Tinie Tempah and producer Route 94. And she has had three solo No 1 singles, Hold My Hand, Don't Be So Hard on Yourself and I'll Be There, from her 2015 debut LP.

Now it's time for her second album, released next month; a new single, All I Am, came out on Friday. "It's quite a daunting prospect. Oh my god, if I don't get to No 1, is everyone going to be like, 'She's failed'?"

Success creates its own pressures. "It can be quite draining when you hear those words 'smash hit'. Because you write a lot of songs, and most of them don't even see the light of day. Every time you write, you never know what's going to happen. You just pray that it works."

Something is clearly working for Glynne. There is an intriguingly British quality to her soulful dance music, the same kind of wholesome determination to deliver an upbeat message that you hear in Beverly Knight, M People and Soul II Soul.

"That's how I was brought up. There was a positive energy in my house."

She was raised in north London, in a close-knit Jewish family in Muswell Hill. "As a kid, all I ever wanted to do was sing. My sister used to be like: 'Shut the f*** up!' I'd be in the shower, belting it out like I was at Wembley. Even my parents would be like: 'Come on, Jess. Think of the neighbours.'"

Her father owns an estate agency and her mother worked for a time in A&R at Atlantic Records. She constantly refers to them in her conversation. "I was always told, growing up: 'Be who you want to be, do what you want to do ... Just don't piss us off!'"

Glynne talks fast, with real energy and candour. She is keen to communicate, although she has a tendency to repeat and contradict herself, and takes frequent recourse to platitudes, particularly "it is what it is" and "I am who I am".

When she can't express a notion in words, she tries to illustrate her ideas by bursting into snatches of song. "I talk too much," she laughs. "You can just cut half of it out."

The same charismatic empathy you hear in her music is visible in her everyday interactions. I watched her in a recording studio, making sure everyone around got what they needed, and knew they were appreciated. She describes All I Am as "a big 'I love you' to the people who make you who you are, stand by you and show you the goodness in life".

First among these are her family. "Your parents teach you what's important. Listen, I've been through ups and downs, and I know it's easy to feel life is overwhelming. But what I love most about music is you can be drowning in your sorrows but you play a song and it can change your mindset completely."

Her 2015 debut album was called I Cry When I Laugh, and even when she was singing about heartbreak she insisted on finding positive messages.

"I want to say it's okay to be sad. I don't want to make dark music. There has to be hope."

It was written after she broke up with a girlfriend, a fact she blurted out in an early interview but has since come to regret for all the questions it raised about sexuality. She has also dated boys, and would rather not have any labels placed upon her. "I don't think it should matter one way or another."

Her forthcoming album is entitled Always Inbetween, which she says reflects her whole personality. "For a while I felt a bit lost. But then I thought, 'It's okay to be in-between, it's okay to love who I want to love, to be who I am in public and be who I am at home, it's all just me'."

She complains there is still pressure on female artists to be sexually revealing. "Men don't get that. There's double standards."

Without criticising any particular artists, she suggests that "part of the problem is girls abide by it. I may not be the most innocent, but I would never wear anything or do anything that felt uncomfortable".

The new album includes a song, Thursday, written with Ed Sheeran, explicitly affirming a message of self-acceptance. "In this business, you are being judged all the time. I'd be lying if I said I didn't feel insecure, like I wasn't good enough or pretty enough, and it wasn't enough just to have my music."

The song advocates turning off social media for a day to slob about. "Instagram and Facebook create so much pressure on kids. Nobody is perfect. People wake up and have scruffy hair and spots on their face, and that is all a part of life."

She and Sheeran are both redheads. "It's weird. I don't understand why there is such a prejudice about it in this country. I've definitely heard all the ginger jokes. But guys get it a lot harder. But maybe people like Ed and me, we're changing that. I love my hair. It is what it is, right?"

Jess Glynne's single All I Am is out now. Her album, Always Inbetween, is released by Atlantic Records on September 21.