"But, if you don't look for it then, let it go dead, then try and 'backdate' your search, can you find anything out?"
Committing a bit a MN sin here by starting with "my DH says", but he used to be a software engineer for a mobile phone company and he says:
The tower receives the packets (chunks of data) from the phone and keeps a record of that via the IMEI, so, yes, if they know the IMEI of people's phones (which they wouldn't know automatically but could find out via finding their mobile numbers and getting the IMEI from the company, so theoretically they could search the big database for the numbers and cross-locate which tower the phone was seen on.