In his opening monologue, host Jack Whitehall described Flack, who died in London on Saturday, as a "kind and vibrant person with an infectious sense of fun".
"She will be sorely missed. I'm sure I speak for everyone when I say that our thoughts are with her friends and family," he added.
Whitehall then introduced Lewis Capaldi performing the Song of the Year, Someone You Loved.
Harry Styles, who dated Flack at the start of his One Direction career, later gave a very moving performance of his ballad Falling. He had earlier been photographed on the red carpet wearing a black ribbon on his lapel.