Amy Winehouse’s struggles to quit drugs were well documented. But her family fears that sudden abstinence from alcohol might have been what led to her death last Saturday at age 27, according to a report.

Winehouse ignored doctors’ advice to step back gradually from her heavy drinking and went cold turkey in the past month, an unnamed family friend tells Britain’s Sun. Her family believes that was too much of a shock to her system, the source adds.

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“Abstinence gave her body such a fright, they thought it was eventually the cause of her death,” says the source.

PEOPLE has confirmed that this is the family’s belief.

The cause of Winehouse’s death won’t be known for weeks, pending the completion of toxicology tests.

There have been reports that Winehouse went on a bender during her final days. But the family source tells the Sun that her father, Mitch Winehouse, said in his eulogy at his daughter’s funeral that he believed it was just the opposite.

“He said doctors had told Amy to gradually reduce her intake of alcohol and to avoid bingeing at all costs. Amy told him she couldn’t do that. It was all or nothing and she gave up completely,” says the source.

“Mitch said the shock of giving up, after everything she had been through over a bad few years, was just too much for her to take.”

• Additional reporting by SIMON PERRY