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The Sun says the pair, who were recently staying in a rehab clinic together, are on a distant island resort which it does not name.
Recent reports suggest they have problems with exhaustion, alcohol and illegal drugs.
Singer Winehouse, who has pulled out of a string of gigs in recent weeks, apparently had to persuade her partner to join her on a flight from Heathrow.
"Blake won’t go back to rehab and she won’t be parted from him, so this was the next best thing," a source told the paper. "At least it gets her away from drugs in London."
