Bristol Airport warned passengers that “disruption is expected” over the weekend and passengers are advised to check with their airline before travelling.
Cardiff Airport said it will not operate flights during the red warning and advised travellers to contact their airline or tour operator.
Both bridges linking England and south Wales – the M4 Prince of Wales Bridge and M48 Severn Bridge – have been closed.
In Wales, all domestic football and rugby matches scheduled for Saturday have been cancelled, as has Cardiff City’s Championship fixture against Watford which had been due to kick off at 15:00 GMT.
All of London’s Royal Parks will be closed on Saturday, including the Winter Wonderland attraction in Hyde Park.
In Northern Ireland, where there is an amber weather warning until 21:00 GMT, multiple Christmas events have been cancelled this weekend.
Belfast City Council said its Christmas market would be closed on Saturday, while the Enchanted Winter Garden events at Antrim Castle Gardens had been cancelled for Friday and Saturday.
Amber weather warnings in Northern Ireland, Wales and western England are in place until Saturday morning, while other parts of the UK have lower-level yellow weather warnings.
Storm Darragh is the fourth named storm of the season following Bert and Conall which caused severe flooding last month.