Burt Bacharach and Sir Elton John are already huge fans of her music.
And with her debut album about to be released and a performance on the opening night of the Electric Proms, Rumer is certain to attract a few more.
The 31-year-old, who was picked by Sir Elton to perform with him at the London gig, is still amazed she will be singing alongside the legend.
"I've never done anything like that before, it's a huge opportunity, a massive deal," she says.
The musician, who is keeping tight-lipped about their song choice, adds: "I'm busy learning the songs and I'm really looking forward to the performance."
Born Sarah Joyce, the singer decided to call herself Rumer because she felt it was a more "glamorous and romantic stage name".
The star chose the name after her late mother left her a list of books she should read.
Unfortunately it went missing and the only author she could remember was Rumer Godden.
"My mother really enjoyed her books and I remember really liking the feel of the name."
Before she became a professional musician, Rumer tried many different jobs from working in a deli to cleaning, but has now found a career she plans to stick to.
After 10 years of gigging and knock-backs, her big break came after a chance meeting with television composer Steve Brown.
He appeared as the band leader in Steven Coogan's Knowing Me, Knowing You and has also written music for various shows including Spitting Image and Harry Hill's TV Burp.
"He really liked what I was doing and he gave me time and threw some money at trying to put some quality songs down," Rumer says.
"Because he was successful and he had his own studio and lots of money he felt benevolent towards me, I think he felt sorry for me."
Unlike a lot of chart artists, Rumer says she decided to avoid appearing on any reality TV shows to help boost her career.
"My mum used to say 'you should go on The X Factor, you'd win it', but I didn't dream of it.
"I think it's brilliant and I enjoy it so much, but I think that X Factor's more about elevation than it is about talent."
Rumer's hard work finally paid off last year when she signed a record deal with Atlantic.
Her debut single Slow reached number 16 in the UK singles chart and she is also releasing a follow-up single, Aretha.
Both songs are rich in sound with thought-provoking lyrics, enhanced by her soft and mellow voice which has been compared to the late Karen Carpenter.
Rumer's album has spent several weeks at the top of the iTunes and Amazon pre-order chart, making chart success likely when it is physically released.
"The proof for me will be when the album comes out and people see the full landscape of the work and how every song has been lovingly crafted," she says.
"A lot of love and friendship went into making the record."
The singer says it is important to her that people "receive the album well and pass it around".
But with Bacharach - one of the world's greatest songwriters - praising her work, surely there can be no better validation?
The musician asked to meet with Rumer and she was flown to his house in Los Angeles.
When asked what he was like, she reels off a list of personality traits.
"He was straight to the point, doesn't suffer fools gladly, he's intense, purposeful, just acutely talented and the greatest living composer of the last century," she says.
"He doesn't have time to placate you nor will he help your ego. He's not interested in that stuff. All he's interested in is beauty and getting there."
Former Deputy Prime Minister Lord Prescott has made his approval of her public on social networking site Twitter.
After watching her recent performance on Later With Jools Holland, he suggested she duet with Mick Hucknall.
His unlikely intervention led to him being asked to write a blog for The Guardian about her and his love for music.
"She sang only one song but it moved me," he wrote.
"There was real sadness and longing in her voice as she sang Slow - a song about a woman having to suppress her emotions for fear of putting off a man."
In return, Rumer is equally complimentary about his piece, saying it was "brilliantly written, very raw and very concise".
The singer says she hopes his appreciation will lead to an invite to perform at the Labour peer's New Year's Eve party - and herald another good year.
Seasons of My Soul by Rumer is released on 1 November. Her single Aretha comes out on 25 October.