Punk icon Sid died of a heroin overdose at the age of 21, after being accused of murdering former lover Nancy in 1979.
Blake's father Giles expressed his worries after Amy and Blake ran away from rehab last Sunday, despite promising him that they would take control of their lives.
"Drink, drugs and a history of self-harm is a worrying cocktail. I'm going to point out the Sid and Nancy comparison to Blake," Newsoftheworld quoted him as saying.
Giles believes that thinking about Sid and his girlfriend may help Blake and Amy mend their lifestyle.
"You couldn't tell Sid Vicious what to do, could you? But I'd like Blake and Amy to think about those two. It might shake them up. I doubt it, but maybe," he said.
In the early hours of Thursday, the couple were seen wandering the West End, with Blake's face covered in deep scratches and Amy sporting an ugly bruise to her neck.
Amy had revealed that the pair had a bust-up after Blake found her about to do drugs with a hooker.
"They've fallen out and Amy's gone a bit frenzied. She's got her claws into his face. Blake's a dignified person. He wouldn't hurt Amy — not even in self-defence. But clearly she's gone hell for leather," Giles said.
"It's nasty. The trouble is Amy does like to have her own way and she can be quite wilful. Maybe she wasn't allowed to continue whatever she wanted to do and this is how she reacted. Blake hasn't been supplying Amy with drugs. But there are people close to her who do," he added.