Lol - I've never seen a tornado in the UK in my life... and I've been observing the weather in the UK on a daily basis for over 5 years... I don't think you need to worry.
No, we have nothing like that in the UK - the weather is broadcast on regular TV (I.e. the news programs) and on regular radio shows. We also have our website, YouTube and our app.
We really don't get enough extreme weather to warrant a whole service for the weather... if there's a big weather event happening, it'll be all over the national news anyway (I.e. St. Jude's storm in 2013, Boscastle floods in 2004, the 'hurricane' in 1987). There was a tornado in Birmingham in 2005 that made the national news because:
a) it was the strongest one recorded in 30 years (F2)
b) it carved a 1km long path through the city
c) it damaged a church and a school, uprooted 1,000 trees and caused £40 million of damage
and
d) it caused 3 serious injuries (no fatalities)
Honestly, I'd probably just leave the radio in the US - I can't see you'll have any use for it in the UK.
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