Southern Electric engineers have been out at first light to restore power to another 4,000 customers. The company says its focus is now on a number of areas with significant damage, and making locations safe before carrying out further work.
Key areas include the rural areas around Basingstoke, Aldershot, Reading and a small number of isolated areas in the New Forest.
West Sussex County Council says it is ready to offer help and advice to vulnerable people who may still be suffering from a loss of power as a result of the storm that swept across the county on Monday.
The council is urging vulnerable people or residents who know of someone in their area affected by this to contact them on 01243 642104.It's believed that in some parts of West Sussex, power supplies may not be back to normal until Wednesday.
Ten thousand homes are still without power after yesterday's stormy weather caused huge disruption across the region.
Worst affected areas include Reading, Basingstoke, Salisbury and the outskirts of the New Forest. Southern Electric's engineers are to back out to restore the supply. Meanwhile rail services, which saw cancellations and delays, are returning normal.