Her and fiancee Dave Fairbairn were both arrested near their home in Broxbourne, Hertfordshire at around 1.30am on Saturday.
Fairbairn was held on a public order offence, and then released.
A Hertfordshire police spokesman confirmed that a 59-year-old woman was caught for drink driving, and that her fiancée was arrested on suspicion of a public order offence.
Dave, 59, has a criminal background - serving time in 2003 for plotting to import ecstasy tablets into the UK. Police found 839,500 tablets during the drugs raid - which at the time was the biggest haul in their history.
Just last week, Gillian, who is most famous for her role as Kathy Beale in Eastenders, revealed that her fiancee is currently suffering with prostate cancer.
In a tragic coincidence, her former husband of 23 years - Geoff Knights - died of the same disease 15 months ago.