The show "Germany, memories of a nation" runs until January, with an iconic 1953 Volkswagen Beetle car gracing the museum's entrance hall.
The post-war vehicle serves as a symbol for a show that seeks to get beyond tired World War II cliches about Germany that have proved particularly persistent in Britain.
"There is this focus especially on the period of the Third Reich, and any section of German history books in Britain will be overwhelmingly dominated by the World War II," Barrie Cook, one of the exhibition's curators, told AFP.
The exhibition confronts that period head on, displaying a replica of the sign outside the Buchenwald concentration camp with the chilling slogan "Jedem das Seine" (To Each His Own).
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But its 200 exhibits draw from very varied periods of German history and include a hat lost by Napoleon in the Battle of Waterloo and a famous portrait of the poet Goethe.
Timed to coincide with the 25th anniversary of the fall of the Berlin Wall on November 9, 1989, the exhibition aims to reflect "a history full of triumphs and tragedies".
Among the assembled objects is a gold clock built by the watchmaker Isaac Habrecht like the one he made for Strasbourg cathedral; a porcelain rhinoceros as a reminder of the city of Meissen's famous craft tradition and a wooden cradle designed by the 20th century Bauhaus school.
The British Museum also tackles the thorny issue of formerly German towns and territories like Strasbourg and Basel or Kaliningrad, that have lost their German populations.
The show has received overwhelmingly positive reviews.
"It's an interesting approach," said Bernhard Schulz, a correspondent for Berlin's Tagesspiegel daily.
"It's not a historical exhibition in the true sense of the word... It is more a history of memories of Germany, of what is focal to the German consciousness in general," he said.
The London Times daily said it offers "myriad antidotes to all those tabloid stereotypes of Europe's most powerful nation".