The car was stopped by police after a member of the public reported that they thought the driver was under the influence of alcohol.
Ashcroft was found to be nearly three times the legal limit when she gave a breathalyser reading at Middlewich police station.
The veteran actress later arrived at the station and was herself arrested on suspicion of drink-driving.
Ashcroft, from Lechlade, Gloucestershire, later pleaded guilty to drink driving and was banned from driving for two years.
Knox was banned from driving for a year, fined £3000 ($6000) and ordered to pay costs of £1750 ($3500).
Last April, Knox denied the charge, but last night she changed her plea just as she was about to be tried in Crewe, South Cheshire.
The BBC Online reported that at a previous hearing, the court heard that because she had been drinking, she was told by police on arriving at the station to see her daughter not to drive home.
The court heard Knox was offered a lift home by police officers, but she declined this as well as ignoring their advice about not driving home.
Judge Brigid Knight, sentencing Knox, said her original not guilty plea had wasted court time and money.
Knox's lawyer, Nick Freeman, accepted the actress was "the author of her own misfortune".
He said his client "considers drink-driving to be serious" and had not sought to justify her actions.
Telegraph Group Ltd, BBC Online