Rover could probably tell us a lot more about that escort era
If your mobile is turned on, your operator knows where it is right now to an accuracy of a few tens of metres in a city centre. You do not need gps, this is done by comparing signal strength as received by the nearest base stations. (There are commercial services available that will provide this information if, for example, a parent wishes to keep tabs on a child or if a company wants to know where its mobile workforce is.)
I am not aware of any operators in the free world who actually keep logs of that data. What they do log however, are the network events. As you move about, your phone steps from one cell to another. Operators hold that info for a short time at least and there have been cases reported recently in which the police have used that data to id a killer. To within an accuracy of an area roughly the size of a football pitch, an operator could tell where you live, work, shop and visit escorts.
If you are interested in a specific mobile phone and are willing to devote some resources to the problem then you can easily identify an individual. Suppose that the authorities want to trace your mobile and they have worked out from the logs that you drive down a certain street on the way to work each morning. They just have to park an unmarked car with numberplate recognition cameras there for a couple of days. They will know your time on the road from the cell switch log. How many cars will show up at the corresponding minute on two days? Just the one I expect.
When investigating a murder, all of those techniques would be used.
If you want to get into the world of Jason Bourne then even the dumbest of gsm phones can be located with an accuracy of between 10 and 40cm as long as it is turned on. That is beyond the reach of regular law enforcement types but it has certainly been proven to work.
Switching SIMs is not enough either as the phone operator also gets the ID of your phone and can spot when you switch SIMs.
On a side note, I observe that a man recently convicted in the UK was identified because he used his Tesco Club Card when he paid cash for his call credit top up.