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.
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Becky Mantin has Thursday's weather forecast for the west of the region.
Becky Mantin has today's forecast for the east of the region.
Doors have been smashed and thousands of pounds in cash, jewellery and camera equipment taken in a spate of burglaries in Farnham, Surrey.