A yellow weather warning has been issued for Cumbria.
Forecasters believe the winds could cause travel disruption, power cuts and damage to buildings in the coming days.
A separate alert is in place across the Midlands, Yorkshire and much of the north on Tuesday evening into Wednesday.
Strong winds and stormy weather are set to batter the capital this week.More news: Hospital In Lockdown After Reported Shooting
But strong winds are still expected and the Highways England warning applies to the whole of the UK.
Nicola Maxey, spokesperson for the Met Office, said the cool weather will bring the risk of hail and thunder by tomorrow.
A chief forecaster's assessment says: "The strongest winds are expected to arrive in the west of the region later on Tuesday evening and move eastwards overnight".
"Low pressure will be in charge with winds really picking up on Sunday night into Monday possibly causing some issues for rush hour".More news: Rush Limbaugh forced to flee "liberal hoax" Hurricane Irma
Road, rail and air services may be affected, with longer journey times and cancellations possible, along with some restriction to roads and bridges.
Gusts up to around 75mph could also be possible in exposed locations such as the coast and hills in these areas, the Met Office said.
People are being warned to keep away from sea cliffs, piers and coastal areas.
These winds are forecast to affect coastal counties in the southwest, south and possibly parts of the east coast later in the day.More news: Cardinals RB David Johnson to undergo wrist surgery
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