Would be interesting to know if you can continue manually in HUD manual CAT III approved 737s in case of an autopilot failure.
In fail operational ones you have to check if above or below 200ft RA, the system and failure logic changes at alert height. For example the NO AUTOLAND message is inhibited, same as NO LAND 3 or LAND 2, and autoland is assured below 200ft, above 200ft it's a mandatory go-around.
In fail passive ones it is a mandatory go-around for all failures except AT disengagement, manual thrust operation is allowed in that case. However the relevant table has a note that manual landings are permitted "If suitable visual reference is established", however it fails to define what a suitable visual reference is.
However it further states for fail passive operation:
• For operations to actual RVR values less than 300m, a go-around is assumed in the event of an autopilot failure at or below DH. This means that a go-around is the normal action.
• There may be circumstances where the safest action is to continue the landing. Such circumstances include the height at which the failure occurs, the actual Visual references, and other malfunctions. This would typically apply to the late stages of the flare.
• It is not forbidden to continue the approach and complete the landing when the Commander or the pilot to whom the conduct of the flight has been delegated, determines that this is the safest course of action.
Autopilot failures are not considered for fail operational planes below 200ft as the system should be able to cope with all failures at that point, besides there is no DH anymore.