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.
Just in: Fawley Power Station is closing in March 2013 after 41 years. It had been due to close in 2015. During its lifetime the power station has provided electricity for millions of homes and businesses across Britain.
Fawley is opted out of the EU Large Combustion Plant Directive, aimed at reducing emissions across Europe, and was therefore required to cease generation by the end of December 2015 at the latest. Due to current market conditions the main units will now close earlier than predicted.
The closure of Fawley reflects the changing shape of power generation in the UK, with modern lower carbon power generation replacing older, less efficient power stations. The future of the site has yet to be decided.