There is severe flooding in parts of Northern Ireland and flood warnings remain in place across England, Scotland and Wales, BBC reported.
"Severe disruption" means Network Rail is advising customers to check before they travel on the railways.
Franklin comes days after Storm Eunice killed three people and left 1.4 million homes without power.
The highest wind gust speeds on Monday morning reached 79mph in Capel Curig in Wales, and 78mph in Orlock Head, Northern Ireland. On Sunday night, 87mph was recorded at the Needles on the Isle of Wight.
The Met Office issued two weather warnings for earlier on Monday: an amber warning for wind in Northern Ireland, and a milder yellow warning for wind covering Wales, Northern Ireland, most of England and parts of south-west Scotland.
Storm Franklin is the third named storm in a week - following Dudley and Eunice - the first time this has happened since the storm-naming system was introduced in 2015.
On Monday evening, UK Power Networks said it had restored electricity to 98% of properties across east and south-east England but 8,500 remained without power.
Energy minister Greg Hands said power outages were a "horrible thing" to happen to households and lessons would be learned for the energy network.
Manchester Airport diverted nine flights on Monday morning because of storm winds. It is understood the planes were holding to land before being diverted, but the airport says the weather has not affected departures.
In Northern Ireland, heavy rain has caused severe flooding, with counties Londonderry and Tyrone the worst hit.
Northern Ireland Electricity said at the peak there were 10,000 homes without power during the early hours of Monday morning - that number has now fallen to around 330.
Parts of the River Severn and the Bristol Channel coast are on flood alert and emergency teams have erected flood barriers to try to stop the waters from reaching homes.
County councillor Karl Lewis said Llandinam in Powys, central Wales, had been left looking like a "disaster zone".
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