Both are possible but with different meanings. The weather in Britain is changing - if this is happening now, or if this is the current trend. The weather in Britain is very changeable - if this is a general statement.
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AnonymousCan is use both variants ?I don't recommend it. No. Use "changeable". "changing" is not really an adjective, so it's odd to hear it with "very". "very changing"?
AnonymousThe weather is often changing in Britain.It's borderline acceptable, but with 'often' I recommend a slightly different version.