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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Tuesday afternoon's weather for the west of the region
Tuesday afternoon's weather for the east of the region
Two private citizens have already paid a "significant deposit" to take the week-long trip.