Can my phone track my movements? Should I not allow this to happen?

A matter of personal choice.

If you’re using maps or navigation on your phone, it is pretty important to allow your phone to know where you are!!

If you don’t want adverts from a coffee chain, perhaps it’s a good idea to disable location services before you go into a cafe!

Or, if you don’t want anyone to know where you are (???) again perhaps a good idea to disable location services.

You can do this in quite a granular fashion, so you can switch off for the device, for the application on the device, or only when using the application on the device. That’s why it’s quite important to close down an application when you don’t need it, or aren’t using it, because it will continue tracking you after you think you’ve stopped using it!

Of course with the Covid-19 tracing capability Google and Apple have jointly worked upon, this relies on an element of location services to be working, but that’s to determine proximity of individuals and as I understand it, location is not stored on any central server.