Back-up generators are providing electricity to Holy Island and will continue to do so until the main power supply cable is fixed.
The cable was damaged last Tuesday and islanders were without electricity for a few hours until the generators were put in place.
A spokesman for Scottish Power said: “Significant damage was done to the sub-sea cable, caused by a third party.
“Residents were only without power for a short period and everyone is now on full supply with generators.
“They will be on full supply until we carry out a complete repair. We apologise to our customers for any inconvenience caused.
The timescale for the work has not been revealed, but the spokesman added: “It is likely we will have to get marine permits and the repair is more difficult because of the type of cable involved.”
It has been suggested locally that the cable was damaged during trench digging on the causeway to reduce the accumulation of sand and sea water along the road between the bridge and Snook End.
However, a spokesman for Northumberland County Council said: “While we are aware of electricity supply issues to Holy Island, neither the county council nor the contractor is believed to have damaged any sub-sea cables and there is no evidence to suggest they are responsible.
“The drainage improvement work is on hold until the supply problem is resolved.”
The £25,000 scheme is being coordinated by the county council in partnership with Natural England, which is responsible for the Lindisfarne National Nature Reserve.
The aim of the work is primarily to remove standing water from the causeway, but it also involves around one hectare of salt marsh being relocated as part of efforts to restore damaged areas.