The MET office said: "Gales, and more locally severe gales, are expected to affect much of the country on Tuesday.
"Whilst Monday night will see wet and windy conditions sweeping eastwards, the strongest winds are expected to occur after the rain clears and winds veer northwesterly through Tuesday morning.
Gusts exceeding 55 mph are likely inland, with 60 to 70 mph gusts in some exposed coastal areas in the west and possibly to around 80 mph around coasts in northern Scotland."
In a formal assessment, the Met Office Chief forecaster wrote that strong winds could cause travel disruption across the UK, particularly during the busy rush hour period.
He said: “The remains of Hurricane Gonzalo are running across the Atlantic, reaching the UK on Monday night, bringing a period of strong winds to the UK.
"The strongest winds are expected on Tuesday as the low pressure clears eastwards; some uncertainty remains in peak wind speeds but there remains the potential for disruption to travel, especially as the strongest winds coincide with the morning rush hour in places.
"Fallen leaves impeding drainage increases the risk of surface water affecting roads, while some damage to trees is possible, given that many are still in full leaf."
The hurricane caused damage when it hit Bermuda over the weekend, and one person tragically died in Saint Martin when it initially made landfall.
Residents in Bermuda were told to stay indoors to minimise casualties.
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