Forecasters are predicting a very windy spell of weather, with travel disruption, power cuts and damage to buildings expected.
Severe amber weather warnings have been issued for the North of England, Scotland and Northern Ireland, which are in place until 5pm on Wednesday.
“Flying debris is likely and could lead to injuries or danger to life,” a Met Office spokesman said.
Commuters have been told to expect longer journey times and cancellations, with road, rail and air travel likely to be affected.
The strong winds may blow tiles from roofs and cause damage to properties from falling trees, the Met Office said.
There is also a risk of power cuts, which could affect mobile phone coverage, it added.
A less severe yellow warning for wind has been issued for the whole of Scotland, northern England, north Wales and Northern Ireland until 10pm.
A yellow warning for rain is in place for northern England and Wales on Thursday as wet weather brings a risk of flooding to some homes and businesses.
Some 40-60mm of rain is expected widely, with up to 80-100mm in parts of Wales and Cumbria.
Storm Ali comes after the UK was hit by the remnants of tropical storm Helene, which brought gusty winds and an unusually warm start to the week.
Sky weather presenter Isobel Lang said: “The weather does not look like settling down for a while yet with a series of Atlantic depressions set to sweep across the country.
“Thursday’s depression is more likely to be a rain-maker with the potential for some local flooding, and another deep low is due over the weekend.”
Ali is first on the storm names list for 2018-19 announced by the Met Office and Met Eireann, which has run the Name Our Storms scheme for four years.
The season’s names have been compiled from a list of submissions by the public, choosing some of the most popular names and also selecting those which reflect the nations, culture and diversity of the UK and Ireland.