No

Why? Because you should be inside at home! #StayHome

But if you absolutely had to go out to get groceries, medication or other essential travel, No, you don't need a jacket.

Based on the weather in Luton, UK as of June 2, 2020 12:16pm local time.

Now

Overcast
Temp: 67°F20°C
Wind: 8 MPH13 KPH
Precipitation: 17% rain

Today

Next 2 hours: No

Next 4 hours: No

Next 8 hours: No

Tomorrow

Yes

Overcast throughout the day.
Low of 51°F11°C, High of 59°F15°C
Wind: 9 MPH14 KPH
Precipitation: 38% rain