Yes

you do need a jacket based on the weather in Woolwich, London, UK 1 second ago

Why? Because it's bitterly cold.
42°F6°C & Partly Cloudy

Wind is 1 mph2 km/h from the W, gusting to 3 mph5 km/h
April 24
7pm42°F5°C2 mph3 km/h WPartly Cloudy
8pm41°F5°C2 mph3 km/h SWMostly Cloudy
9pm39°F4°C3 mph4 km/h SMostly Cloudy
10pm38°F3°C3 mph5 km/h SWMostly Cloudy
11pm38°F3°C3 mph6 km/h SWMostly Cloudy
April 25
12am38°F3°C4 mph6 km/h SMostly Cloudy
1am39°F4°C4 mph7 km/h SCloudy
2am41°F5°C5 mph7 km/h SCloudy
3am43°F6°C5 mph8 km/h SCloudy
4am46°F8°C6 mph10 km/h SWMostly Cloudy
5am50°F10°C8 mph13 km/h WPartly Cloudy
6am53°F12°C8 mph13 km/h WPartly Cloudy
DateLowHighWindDayNight
April 2341°F5°C50°F10°C6 mph9 km/h from NMostly CloudyPartly Cloudy
April 2438°F3°C55°F13°C7 mph11 km/h from WRainRain
April 2540°F4°C53°F11°C5 mph8 km/h from NECloudyRain
April 2643°F6°C56°F13°C8 mph13 km/h from NEDrizzleRain
April 2747°F8°C56°F14°C11 mph18 km/h from SWRainPartly Cloudy
April 2844°F7°C59°F15°C8 mph14 km/h from SMostly CloudyPartly Cloudy
April 2947°F9°C63°F17°C8 mph13 km/h from SEMostly CloudyMostly Cloudy

Yes

Low of 37°F3°C, High of 55°F13°C
Wind: 7 mph11 km/h
Precipitation: 37% rain

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