According to the Met Office, 'strong and at times gusty winds' are expected through much of tomorrow.
Gust of around 56mph are forecast.
A Met Office spokesman said: "There is a small chance of injuries and danger to life, as well as minor property damage, from flying debris.
"There is a small chance of transport delays, route and bridge closures, and cancellations to public transport."
Meanwhile, today thickening cloud will bring rain, which will be heavy in places, from around 10am.