A spokesman said: "Westerly winds are expected to increase during this evening into the early hours tomorrow morning with gusts in excess of 60 miles per hour possible over exposed roads during the night".
Met Éireann has issued a yellow weather warning for Limerick as it expects a depression to hit Ireland tomorrow afternoon.
Powerful winds threaten damage to trees and buildings with gusts in some parts strong enough to knock out power supplies.
Weather warnings for strong winds and heavy rain have been issued for much of southern Scotland.
Nearly half of the average rainfall for September could fall in six to nine hours from about 4pm on Tuesday, which "seems likely to lead to flooding of some sections of road and perhaps also properties", the Met Office said.
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"The biggest effect from this storm will be the possibility of damaging winds".
But strong winds are still expected and the Highways England warning applies to the whole of the UK.
Temperatures will dip below average for the time of year with highs of just 19C (66.2F) in the south and 15C (59F) elsewhere.
"Some of these could be gale-force touching 50 knots [57.5 mph] as we go into a period of unsettled weather".
Heavy showers are expected throughout Monday and overnight into Tuesday.
Scotland is more at risk of hurricanes this autumn - as the Met Office projected up to 16 Atlantic tropical storms, the most since 2012.