Find My Phone app, with Bluetooth, with mobile data only?

However the family are still under the impression, that the missing mobile could be anywhere within 1 kilometre of this given address.

Find My displayed the last know location for a few days. After that, if the location has not been updated, Find My will display a No Location Found message. The phone could be anywhere if that message is displayed.

I understand Bluetooth is required to be ON to locate an iPhone via the Findmy app

No, that is not correct. Bluetooth can help with location information, but it is not required if a good cellular signal or Wi-Fi signal is present in the area where the iPhone is located.

also I assume IF it is true and you can locate without Bluetooth being on, it will mean that the location may not be as accurate is my understanding correct?

No, not in my experience working with Find My over the years. I just ran another quick test to locate my wife's iPhone, the displayed location information is the same no matter whether Bluetooth is on or off.

Now......if the phone has been powered off.....AND.....Bluetooth was enabled.....then the phone sends out a very brief intermittent Bluetooth signal that can be picked up by other iOS devices or Macs in very close proximity to the iPhone and the location of that device is forwarded to the Internet to help Find My try to locate the iPhone.

This is how Find My may be able to locate an iPhone even if it has been powered off. But this also assumes of course that the iPhone battery has not run down.

Good luck in your search.