After an array of menacing beasts from the sea over the years, we switched a bit last year to a slug-plant hybrid monster. And from there, it's only a shuffling skip-step to Day of the Triffids--a post-apocalyptic film where when it rains blinding meteor showers, it pours mobile, deadly plants. Based on the book by John Wyndham (who brought you The Midwich Cuckoos, which became the film you know as Village of the Damned), it was filmed twice more as TV miniseries.
And honestly, if When Animals Attack makes sense as a subgenre, then When Plants Attack is the logical next step. Enjoy.
Triffids is available on DVD in multiple releases but this appears to be the only widescreen one. So.