Storm Barra is expected to bring ice, wind and rain – which could cause flooding for parts of the UK on Wednesday.
Thousands of homes lost power for up to 10 days in the wake of 100mph winds and lashing rain at the end of November.
Northern Powergrid has not confirmed whether all homes were connected by Tuesday night as promised.
Storm Barra moved in from the west on Tuesday, and a yellow weather warning for wind is in place from midnight until 6pm on Wednesday for the west coast of Wales and south-west England.
Aberdaron in Gwynedd, Wales, which is covered by the warning, was battered by gales of 86mph on Tuesday, while Orlock Head in Co Down, N Ireland, faced 76mph gusts.
Met Office forecasters said Storm Barra is not expected to cause as much chaos as Storm Arwen – though it has already sparked travel delays and school closures in Scotland.
Spokeswoman Nicky Maxey said: “We are not expecting the impacts of Barra to be as bad as we saw with Arwen.
“Storm Barra will bring strong winds and heavy rainfall to many parts of the UK today.
“We may see some snow on the higher ground, too.
“It is unlikely to be as impactful as Storm Arwen last week but there will be blustery conditions so people should still be prepared.”
ScotRail has warned that some Wednesday services will be cancelled due to the storm.
Temperatures will be mild for the time of year on Wednesday, with London predicted to see 7C, 8C in Cardiff, 4C for Edinburgh and 6C in Belfast.
The Environment Agency has issued 11 flood warnings for England at locations including Hartlepool and Sunderland in the North East, Bournemouth and Weymouth in the South, and part of the Cumbrian coast.
Some 66 flood alerts, for areas where flooding is possible, have also been issued across the country.
The Scottish Environment Protection Agency (SEPA) has sent 11 flood alerts and five warnings for areas in the north-east of Scotland and the south-west.
Natural Resources Wales has also issued 12 flood warnings and 11 alerts, mainly covering coastal areas.
On Monday, Prime Minister Boris Johnson said more than 1,000 homes were still without power but that he was assured by Northern Powergrid boss Phil Jones that “affected properties would be reconnected tomorrow (Tuesday) at the latest”.
Mr Johnson said “too many people have spent too long without power” and the situation in northern England was not acceptable.
Schools in Dumfries and Galloway were forced to close because of the weather.
Stranraer Academy was shut after the wind caused structural damage to the roof, the council said, and Drummore School closed after trees were blown down.