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Rex Features
The group has cancelled forthcoming live shows, including a slot on the John Peel Stage at Glastonbury.
In a statement on their official site, the band said: "On June 9, Dorian was rushed to hospital after falling ill, and he is still in hospital in Sheffield in a serious condition.
"Because of this, we will regrettably be cancelling all our live appearances until the end of July. Dorian is improving slowly and we will keep you updated on his condition."
The band asked fans to leave messages of goodwill for Cox on their Facebook and MySpace pages.
At present, the Sheffield rockers plan to return to touring in August.
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