The series, co-produced by the BBC Drama and WGBH, is the only UK show in the running for best mini-series or film made for TV. The other nominees in the category are John Adams, Recount, Bernard & Doris and A Raisin in the Sun.
Judi Dench is up for best actress, while co-star and Bafta winner Eileen Atkins is nominated as best supporting actress.
In the film awards, there is a strong showing for Film4.
Channel 4's film arm is up for nine awards - four for Danny Boyle's Slumdog Millionaire, three for Colin Farrell comedy-thriller In Bruges and two for Mike Leigh's Happy-Go-Lucky.
TV dramas nominated this year are serial killer drama Dexter, shown in the UK on ITV1, Channel Five hit House, AMC's Mad Men, shown here on BBC4, plus HBO's In Treatment and True Blood.
In the musical or comedy category, 30 Rock and Californication, both Channel Five shows in the UK, square off against ITV2 comedy hits The Office and Entourage, as well as Weeds, a staple of Sky One's schedules.
The winners of both the TV and film Golden Globes will be announced on 11 January.