It warned people should expect travel delays and power cuts, as well as large waves along coastal roads and sea fronts.
A 24-hour yellow warning for wind covering the entire country comes into place at 00:00 GMT on Sunday morning.
The Met Office extended its amber warning for Sunday to cover most of England and Wales from 08:00, advising that debris and large waves could pose a danger to life.
There have also been yellow warnings for rain issued for Northern Ireland and parts of Scotland from 15:00 GMT on Saturday, extending to include Wales and northern England from 00:00 GMT on Sunday.
Network Rail has imposed a blanket speed restriction of 50mph across the network on Sunday, warning passengers to only travel by train that day "if absolutely necessary".
It said there was the potential for damage to overhead lines and tracks caused by debris or fallen trees.
Avanti West Coast, London North Eastern Railway and South Western Railway were among the train companies which said customers with tickets for Sunday would also be able to use them on some services on Saturday or Monday.
Grand Central cancelled all its services on the East Coast Main Line on Sunday.
Elsewhere, the London Winter Run 10k event - due to be attended by 25,000 runners - was cancelled after organisers said they were "not able to guarantee the safety of our runners, crew and volunteers".
In January, Storm Brendan swept into the UK, leading to power cuts and travel disruption in parts of the UK.
This year's storm names have already been chosen with Dennis the name for the next storm.