Just to be absolutely clear on this one, the police have made no such comments about mobile phone data. The best we have is "a source" to The Sun newspaper that suggested that there was no mobile or "GPS data" and made some conclusions about the perpetrator leaving the mobile at home. I have many doubts about that source because the quotes were technically incorrect although it is perfectly plausible that a determined perpetrator would not take their mobile or switch it off during relevant times. This doesn't raise an illegal immigrant as a suspect in my mind.
I've also said in an earlier comment that mobile phone data is a needle in a haystack to interpret. It gets such a high profile because in serious crime court cases it is used retrospectively to confirm the suspect was / wasn't at certain location but that is once they have a particular mobile phone associated with an individual.
In terms of the data available now, the police can easily obtain a list of all mobile phones connected to local masts during the time of the murder, that will run into thousands of records and cover many square miles in rural locations. There is some ability to triangulate mobile phones to narrow down the location but this will not be particularly accurate in rural areas where transmitters are miles apart, the whole of Aylesham and Snowdown are probably served by the same masts.
The best the police could do would be look at mobile phones connected in the area that moved to another area shortly after the crime occurred but even then they would probably find a list of hundreds, some of which will be unregistered and untraceable. They can't go knocking on the doors of the hundreds of mobiles phone owners that left the area around the time of the crime without something more substantial to connect them to the crime.
Finally the whole "GPS data" comment gets my goat, there is no centrally held GPS data, only the device that uses GPS 'may' have a record of the location. The satellites that provide GPS location have no awareness of who or what is using them or indeed where.
