The film portrays an alliance between gay rights' campaigners and pit workers during the 1984 and is largely set in the Dulais Valley in south Wales.
Writer Stephen Beresford and producer David Livingstone received the award at the ceremony in London on Sunday night.
Beresford said it had taken him 20 years to persuade anyone the story would make a "sure fire comedy smash".
The miners' strike drama Pride has scooped the outstanding debut award at the Bafta Film Awards.