Northern Powergrid first received reports of widespread problems in the LS14 and LS15 postcodes in the early hours - and the problem is still not fully fixed.
As many as 500 homes in Scarcroft, Seacroft and Shadwell were without power at around 10.30am, almost eight hours on from the initial problems.
In its last update, the company said: "We’ve restored supply to most customers in LS14. We are working to have all remaining customers sorted by 11am."
But around 120 properties are still without power now and are expected to be kept waiting until as late as 1pm for their supplies to be restored.
The problem has been linked to a fault with an underground cable in Scarcroft.
Engineers had restored power to all homes affected in LS15 by around 2.45am and the majority of affected homes in LS14 before 5am today.