The pair have previously worked together on the films "The Winter Guest," "Sense and Sensibility" and "Love Actually," as well as several Harry Potter movies.
The BBC said Thompson and Rickman will play former lovers who reconnect in "Lunch," which is to air on Britain's National Poetry Day, Oct. 7.
"We hope that audiences will enjoy this dramatization of Christopher Reid's touching and witty poem, and maybe feel inspired to indulge in a little more poetry themselves," said BBC Two controller Janice Hadlow.
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