Yes

you do need a jacket based on the weather in Royal Leamington Spa, UK 1 second ago

Why? Because just cool enough for a jacket, but not warm enough to ditch it and it's so windy, your hat will probably launch into orbit!
55°F13°C & Windy

Wind is 16 mph26 km/h from the East, gusting to 29 mph46 km/h
April 19
7am56°F13°C17 mph27 km/h EastWindy
8am56°F14°C17 mph27 km/h EastWindy
9am57°F14°C16 mph25 km/h EastWindy
10am58°F14°C16 mph25 km/h EastWindy
11am59°F15°C15 mph24 km/h EastWindy
12pm58°F14°C15 mph24 km/h EastWindy
1pm57°F14°C16 mph25 km/h EastWindy
2pm54°F12°C15 mph24 km/h NortheastMostly Cloudy
3pm51°F11°C15 mph23 km/h NortheastMostly Cloudy
4pm48°F9°C13 mph22 km/h NortheastPartly Cloudy
5pm46°F8°C13 mph20 km/h NortheastPartly Cloudy
6pm45°F7°C11 mph17 km/h NortheastPartly Cloudy
DateLowHighWindDayNight
April 1844°F6°C59°F15°C15 mph25 km/h from EastWindyPartly Cloudy
April 1940°F4°C60°F16°C9 mph15 km/h from EastPartly CloudyMostly Cloudy
April 2043°F6°C59°F15°C6 mph9 km/h from SouthwestDrizzlePartly Cloudy
April 2141°F5°C59°F15°C8 mph13 km/h from WestMostly CloudyRain
April 2246°F8°C62°F17°C7 mph11 km/h from EastRainPartly Cloudy
April 2343°F6°C61°F16°C6 mph10 km/h from NortheastMostly CloudyPartly Cloudy
April 2446°F8°C61°F16°C6 mph10 km/h from EastMostly CloudyMostly Cloudy

Yes

Low of 39°F4°C, High of 60°F16°C
Wind: 9 mph15 km/h
Precipitation: None

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