"I left it at home" is common, but doesn't have the exact same meaning. Tbh, I don't think there really is a way to say that succinctly in British English—we would probably say "I left it at home", "I forgot to bring it", or—if the full meaning is strictly necessary—"I forgot it, it's at home".
Really, "I forgot it at home" is short for "I forgot to bring it; I left it at home".
"I left it at home" is common, but doesn't have the exact same meaning. Tbh, I don't think there really is a way to say that succinctly in British English—we would probably say "I left it at home", "I forgot to bring it", or—if the full meaning is strictly necessary—"I forgot it, it's at home".
Really, "I forgot it at home" is short for "I forgot to bring it; I left it at home".