The TNT Boeing 737 departed Liege (LGG) on an early morning cargo flight to Stansted (STN). Visibility at the destination airport was poor and had decreased below minima. The 05:20 METAR reported a visibility of 250 m, runway 23 RVR of 450 m in fog. The crew entered a holding pattern to await an improvement in the weather. After 30 minutes in the hold and with continued deterioration in the visibility, the flight crew decided to divert to East Midlands (EMA). The weather at East Midlands required the crew to conduct a Category IIIA approach to runway 27. The approach was uneventful until, at approximately one mile from the runway threshold, the autopilot was momentarily disconnected and re-engaged. The aircraft then went above the glide-slope before developing a high rate of descent. At the same time, it deviated to the left of the centre-line. A go-around was initiated but the aircraft touched down heavily on the grass area to the left of the runway threshold. The right main landing gear broke off, causing damage to the right inboard flap, wing/body fairing and rear freight hold door and resulting in the loss of hydraulic System ‘A’. The aircraft continued for a short distance with the right engine, right outboard flap track fairing and right wing tip in contact with the ground before lifting off again. A Mayday was declared and the crew diverted to Birmingham (BHX) where weather conditions were good. An emergency landing was carried out on runway 33 at 05:02. During the subsequent ground roll, the right engine sustained further damage but the aircraft came to rest on the runway supported by the left main landing gear and right engine. CAUSAL FACTORS: 1. ATC inappropriately transmitted a company R/T message when the aircraft was at a late stage of a CAT III automatic approach. 2. The commander inadvertently disconnected the autopilots in attempting to respond to the R/T message. 3. The crew did not make a decision to go-around, when it was required, after the disconnection of both autopilots below 500 ft during a CAT III approach. 4. The commander lost situational awareness in the latter stages of the approach, following his inadvertent disconnection of the autopilots. 5. The co-pilot did not call ‘go-around’ until after the aircraft had contacted the ground. CONTRIBUTORY FACTORS: 1. The weather forecast gave no indication that mist and fog might occur. 2. The commander re-engaged one of the autopilots during a CAT III approach, following the inadvertent disconnection of both autopilots at 400 ft aal. 3. The training of the co-pilot was ineffective in respect of his understanding that he could call for a go-around during an approach.