A yellow warning for wind covers Scotland, Northern Ireland, northern England and north Wales on Saturday.
It then expands to include the whole country on Sunday, while there is an amber warning for England and Wales.
Forecasters have warned there could be travel disruption, with rail passengers being urged not to travel on Sunday.
Several rail firms announced they would operate reduced timetables with speed restrictions being imposed.
The Met Office’s Frank Saunders said winds would increase during Saturday across Northern Ireland, Scotland, northern England and Wales before turning very windy across the rest of the UK through the early hours of Sunday morning.
He said gusts of 50-60mph were expected quite widely across inland areas, with gusts of 80mph or higher in coastal areas, especially south-east England and northern Scotland.
The Met Office’s yellow weather warning for wind – meaning travel disruption is likely – is in place from midday on Saturday.
It covers Northern Ireland, Scotland, northern England and north Wales.
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.
Other things affected include:
The London Winter Run 10k – due to be attended by 25,000 runners – was cancelled;
London’s eight Royal Parks, which include Hyde Park and Regent’s Park, will close on Sunday;
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.