The company will argue that despite heavy rainfall in many parts of Britain, the most drought-affected areas of its region have still had hardly any in the past few weeks and reservoir levels remain critically low.
It is understood that the emergency drought order sought from the Department of the Environment will cover Bradford and Halifax. The department has already granted four drought orders to Yorkshire Water, one of which restricts car washing and watering of parks and sports grounds in Bradford and part of west Leeds.
The new order would allow rota cuts, with homes being cut off for one 24-hour period then supplied for the next 24 hours. Such restrictions are extremely rare in Britain, although they have applied this year in some parts of Northern Ireland.
The Department of the Environment has granted a total of 15 drought orders this year, mostly giving companies powers to take extra water from rivers.