The UK was hit with winds peaking at 85 mph on Tuesday, before conditions calmed down overnight.
Engineers worked through the night trying to restore power to home in Wales, the Midlands and in Southern and Eastern England.
Rail services are still disrupted due to damage caused by the high wind speeds.
The highest wind speeds on Tuesday were recorded in Aberdaron 85 mph, Lake Vyrnwy 83 mph, Pembrey Sands 79 mph and Mumbles Head 77 mph before Storm Barney left the UK around 02:00 GMT
Barney is the second UK storm considered strong enough to be given a name under a new system introduced by the Met Office and its Irish counterpart Met Eireann.
For more information on UK storms please visit www.metoffice.gov.uk/uk-storm-centre/