Fiennes and Rickman have both recorded video messages for the British leader, urging him to take notice of political prisoners being held in the Eastern European country under the rule of autocratic President Alexander Lukashenko.
In his video, Fiennes says, "Today, I appeal to David Cameron, prime minister of my country, to use the power of morality in politics, to disturb the sleep of conscience and urge Alexander Lukashenko, Europe's last dictator, to end the torture of his own people and release all political prisoners before the new year."
Absolutely Fabulous star Joanna Lumley has also filmed a message for Cameron, along with Mark Rylance, Simon Callow and Sir Tom Stoppard, who says, "Democracies ought to be trying to make democracy contagious... The Belarus problem hasn't gone away - it's got worse."
The drive has been organised by members of the Belarus Free Theatre as part of the Free Belarus Now campaign.