Joanna Bushell, 39, of Friars Garden in Stafford, was stopped on the Queen Elizabeth II Bridge on August 6 last year.
She was driving whilst disqualified and had no insurance.
A blood test indicated she had taken cocaine and was also three times over the legal alcohol limit, court documents state.
Bushell appeared at Medway Magistrates’ Court on January 31, 2024.
She pleaded guilty to drink driving, drug driving, driving without insurance and driving while disqualified.
Sentencing was adjourned for a pre-sentence report to be prepared.