The star was honoured for her multi-million selling album, 25, which emerged last year after a long struggle with writer's block.
She was unable to accept the award in person, having played in Zurich, Switzerland, on Wednesday night.
But in a video message, she said he was "very grateful."
"I won it on my last album as well... but I was secretly pregnant, so I didn't enjoy the night too well," she added.
"To win it this time is truly, truly humbling."
Damon Albarn won the lifetime achievement award, in recognition of an eclectic body of work that spans rock, pop, rap, world music and opera.
Presenting the award his Blur bandmate, Graham Coxon, said Albarn had already "fitted in two lifetimes of work... so far".
The star then delivered one of the most well-received speeches of the day.
"What is songwriting? What is it all about?" he said. "True songwriters are people who are able to release themselves from something that's really affected them by writing a song about it.
"Some of us see it as going to church, some of us see it as going to work, but at the end of the day, if you're not connected to the spirit you're not making true music.
"Thank you for this extraordinary, life-affirming honour."
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