Heine's early reputation in England was that of a nihilistic, radical atheist, a blend of the most dangerous elements of Byron and Shelley. How this was pulled even from his satirical writings is not clear to me. Thomas Carlyle described Heine as "(redacted anti-Semitic slur)
Still, when we take a look at Heine's long poem Germany - A Winter's Tale (1844), we can get an idea of Heine's bite. The poet encounters the spirit of Hamburg, his home town. After mistaking her for a prostitute, she offers to give him a vision of the future of Germany. Just stick your head in that toilet, she says. The poet does, but won't tell what he saw, just what he smells:
It turns my stomach still to think
Of those odors blended together -
A cursedly vile foreshadowing smell -
Rotten cabbage plus Russian leather.
This is from Caput 26, p. 532 of the Hal Draper Complete Poems of Heinrich Heine. I do not believe that it requires much interpretive comment.
The slightly earlier satire Atta Troll stars the titular dancing bear. It's a rich, complicated poem, with witches, the Wild Hunt, and attacks on rival poets. Here's a sublime moment where Atta Troll, having escaped from his circus master, tells the other wild bears about his adventures:
Oh, the vanity of artists!
The old dancing bear is beaming
To recall the time his talents
Were dispalyed before the public.
Overcome with his vainglory,
He would like to prove in action
That he is no braggart
But a dancer of great prowess -
So he suddenly leaps up and
Rears himself upon his hindpaws,
And starts dancing, as he used to,
The gavotte, his favorite measure.
Mute, with muzzles gaping open,
There the bear cubs watch in wonder
As the father leaps and capers,
Prancing strangely in the moonlight.
Draper, p. 429.
Here are two other translations of the marvelous Atta Troll: from Google books, a 1914 version, complete with illustrations and the scanner's thumb, and a more recent attempt.
* Quoted in Sol Liptzin's The English Legend of Heinrich Heine (1954).