Wind speeds reached up to 106 mph during Storm Katie, which battered the UK on Sunday evening.
SEPD said it expects the final 200 customers without power in Aldershot, Petersfield, New Forest, Basingstoke and Slough to be reconnected by lunchtime today (29 March).
The firm said it has been calling affected customers to keep them updated on ongoing repair works, and offered alternative accommodation and food to customers it was unable to immediately reconnect due to safety concerns.
SEPD’s director of customer operations Stuart Hogarth thanked customers for their patience and apologised for the disruption and inconvenience that they faced on a Bank Holiday.
He said: “Our customers have been really understanding of the conditions that faced our engineering teams since night.”