The yellow warning remains in place until 1pm on Monday.
Andy Page, Met Office chief meteorologist, said: “Following the significant impacts of Storm Eunice on Friday, Storm Franklin will bring further high winds although not on the same scale as Eunice.
Storm Franklin means further travel disruption is possible again on Monday morning with delays to public transport and some roads being closed.
Power cuts are also possible, as is further damage to buildings and more trees could be brought down.
Rod Dennis, RAC breakdown spokesperson, said: "With winds still strong and gusty, it’s important drivers don’t take any chances, so we urge them to slow down and leave plenty of space between themselves and the vehicle in front.
"If conditions get particularly bad again, people should consider postponing their journeys, and for those who have to drive, it’s vital they keep their wits about them at all times.”
The country is still trying to clear up from the damage caused by Storm Eunice which saw several buildings damaged across the UK and severe travel disruption, notably on the railways where East Midlands Railway ultimately suspended mainline services between Nottingham and London St Pancras during Friday afternoon.
Commuters are advised to check the website here for news of any further service disruption on the trains.