Patricia Menzies

 was a detective inspector for the Salford constabulary in at least the early 21st century.

She met the Doctor when she arrested him for murder. Gradually, she came to understand that he was not a criminal, but a time traveler who could help her uncover the truth of the murder, which involved several aliens who had invaded Manchester. (BFA: The Condemned)

She re-encountered the Doctor and Charlotte Pollard a short time later, when a pound coin from 2012 appeared in a coin-operated vending machine a few years too early. That anachronistic coin led she, Charley and the Doctor into the middle of a war between the Cyrox and the Tabbalac, with Earth as its battleground. After the war was ended, Menzies asked the Doctor if she could travel with him. The Doctor politely refused, citing the growing mystery surrounding Charley's true identity, but indicated that one day he might take her up on the offer. (BFA: The Raincloud Man)

Personality
Menzies was possessed of an earthy, sarcastic personality, somewhat fueled by her love of a good pint. She was a generally by-the-book detective, but could, when necessary, break the rules if she thought it would help her get to the truth of a case. Specifically, she allowed the Doctor, although a murder suspect, access to the evidence against him on the hunch that he might have been able to help her find some answers. (BFA: The Condemned) This severe breach of protocol was met by a stern reaction from her boss, DCI Turnbull.

This wasn't to say, however, that she followed the Doctor's lead blindly. Indeed, she found it necessary on occasion to reign the Doctor in when he was proceeding with his investigations in a way that wouldn't produce evidence that could stand up in court. (BFA: The Raincloud Man)

Her reaction to the true nature of the Doctor's "police box" and to his own alien-ness was matter-of-fact. She quickly grasped some of the fundamentals of time travel, and treated alien threats as any other criminal problem that she might have to deal with in the normal course of her duties.