Latest figures show there are still about 3,500 homes in the South East without power since the storm struck on Monday October 28.
UK Power Networks said some counties were back to normal by yesterday, including Bedfordshire, Buckinghamshire, Norfolk and Cambridgeshire.
Engineers aim to have 98 per cent of power supplies which were affected by the storm restored by the end of today and to the final few by the end of the week.
UK Power Networks said the engineers restored power to more than half a million customers within a day, after high winds caused extensive damage to power lines.
Director of customer services Matt Rudling said: “I would like to thank people who are still without power for their patience, and stress that we are working to restore all supplies as quickly as is safely possible.
“A lot of hard of work is going on round the clock and we are making good progress with repairs.”
The storm was the biggest the company had coped with since 2002, and it caused extensive damage to overhead power lines affecting electricity supplies to nearly 650,000 customers.
Other similar companies across the UK are lending their staff and engineers are currently working with UK Power Networks from Yorkshire, Liverpool, South Wales and the Midlands.
About 1,000 engineers are working hard to repair the damaged network and restore power to customers as soon as possible.
The company said that was six times the usual number on duty.
It is also carrying out helicopter patrols to check overhead power lines.
Anyone spotting a damaged power line is urged to report it to UK Power Networks and advised to stay well clear.
Customer service staff and volunteers from the British Red Cross, which works in partnership with UK Power Networks, are also on site helping people in the worst affected areas.
On Monday the company received more than 157,000 calls and today it says its lines are still extremely busy.
It is asking customers to report any power cuts and damaged lines on free helplines: in the South East call 0800 783 8866.
You can also see www.ukpowernetworks.co.uk and follow the company on twitter for updates.
UK Power Networks said the electricity network was built to be resilient but extreme weather could see wind-borne debris being blown onto overhead power lines.
The company said it activated the early stages of our emergency plans on Friday and brought in additional staff covering engineering, technical and call centre roles.