More than 2,000 homes were without power and a number of roads have been closed in Wiltshire due to Storm Ciara.
Scottish and Southern Energy said areas affected included Tidworth, Warminster, Chippenham, Marlborough, Calne, Devizes, Tisbury and Swindon.
Some 254 homes in Somerset were also without power.
About 1,500 homes have had power restored and “engineers are doing all they can” to reconnect the remaining 500 properties.
Duncan McDonald, from Scottish and Southern Energy, said: “We’re hoping to get everyone back on early to late evening but we’re not out of the woods yet with the weather.
“But we really are doing our best in very challenging conditions to get these customers’ power back on.”
A tree has been cleared from the railway between Swindon and Cheltenham but replacement road transport remains in place.
Wiltshire Council has closed a number of roads and the storm has caused difficult driving conditions on the motorways.
Adrian Hampton, from Local Highways, said they had been dealing with “20 reports every half an hour”.
“We’ve still got trees coming down, it is slowing but we’re anticipating it going on, with really strong gusts, until about 9pm,” he said.
“One major [incident] we’re dealing with is the A3421 near Bowood, with the electricity cables down. All the rest are passable with care.”
He said there had also been a “spate of trampoline incidents” across the county with many being blown on to roads.
People are being advised to ensure their trampolines are “firmly secured”.
Paul Gentleman, from Great Western Railway, said there had been “several incidents of trees falling across the line”.
“The line between Swindon and Cheltenham was closed partially earlier on today while a tree was cleared there,” he said.
“But with the weather like it is at the moment, it’s very difficult for crews to work safely clearing the debris and getting lines re-opened again.”