Crime Traveller

Crime Traveller was a short-lived British television series from The Nineties, created and written by Anthony Horowitz. Police detective Jeff Slade discovers the existence of a time machine (maintained by Holly Turner, daughter of the inventor) that can be used to travel up to a day into the past. Slade teams up with Turner and they start using the machine to solve crimes by visiting crime scenes as the crime is occurring.

Note that using the time machine to prevent the crimes isn't an option: The past is fixed, and any attempt to alter things results in the discovery that You Already Changed the Past. It happens more than once that a crime will have some odd detail which turns out to have been caused by Jeff Slade in his attempt to solve it.

Tropes used in Crime Traveller include:

Amateur Sleuth: Holly kind of fits this trope, since she's more of a scientist than a proper policeman.
Awesome McCoolname
British Brevity: The only season had 8 episodes. There were ideas for a second season, but the BBC wasn't impressed and axed it (like many other of its sci-fi shows from the late 90s).
Clear My Name: Episode 2, with the variant that they have five hours to do it and get back to the time machine. Also present in Episode 5.
Never the Selves Shall Meet: It's not known what would happen if a time traveller met himself, but it's taken for granted that it would be bad. Probably a good idea.
Set Right What Once Went Wrong: Averted. They're not trying to explicitly change history, just learn more about the details of any mysterious/uncertain case, so it could get properly investigated.
Shout-Out: In Episode 6, Jeff is discussing a case with another officer, and says that "I've got another line of investigation"...while looking at a certain blue box.
The Slow Path: Since the time machine can only be used to travel into the past, the traveller can only get back to the "present" by the same method as everybody else. Good thing it's got such a short range, eh?
- Of course, the physics of time travel do mean that anything that changes you between departure time and being at departure time again resets, such as the cut to the forehead that Slade receives in the first episode. Even if you do age after a time jump, you will revert back to the age you were to begin with.
- There's a catch though: Miss the time limit left for you to return to the machine and you'll end up in a Stable Time Loop forever. Holly's father Frederick supposedly ended up like this, so he's not really dead (as if that was any reassurance). To prevent the the two detectives from not returning on time, they carry a special countdown wristwatch - and, as per Rule of Drama, it gets accidentally lost in one episode while the characters are on the run, further complicating matters...
They Fight Crime: He's an ordinary London police detective, she's a police science officer who inherited a time machine created by her father. Together, they solve cases by travelling back in time.
Time Travel: In theory, it's all Stable Time Loop and You Already Changed the Past...but in practice, slip-ups by the writer sometimes result in Timey-Wimey Ball moments. Oh, and you cannot travel into the future, since it hasn't occurred yet (unless you travel to the past and catch up with the point of "present" you departed from).
Wrongful Accusation Insurance: Episode 5. Slade is accused of stealing diamonds. He resists arrest, shoves people aside to escape (which is battery), and steals a car to escape. Note that Slade is a police officer and still manages to keep his job after this, never mind being not sent to jail for the crimes.