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 East Molesey, UK as of June 1, 2020 8:48pm local time.

Now

Clear
Temp: 69°F21°C
Wind: 7 MPH12 KPH
Precipitation: None

Today

Next 2 hours: No

Next 4 hours: No

Next 8 hours: Yes

Tomorrow

Yes

Partly cloudy throughout the day.
Low of 54°F12°C, High of 78°F26°C
Wind: 6 MPH10 KPH
Precipitation: 1% rain