It's BT Openreach telephone wiring but these are also used to deliver DSL broadband (ADSL or VDSL/FTTC). You and your neighbours may not have a telephone but they may have broadband. I would not disconnect it unless you are sure that there is nothing on the end of it.
In the most recent Openreach implementations (SOGEA and SOTAP) there is no analogue phone service on the line any more, only DSL, and the phone service is provided via VOIP ('digital voice') This means you may be unable to measure line voltage or detect a dialling tone. I believe there may be still some 'wetting' voltage on the line (to detect/prevent high resistance faults) but not necessarily full ringing voltage as mentioned in another answer.
Legally speaking it belongs to Openreach and that would count as damage to their property. However in practice it would likely be fine to move it a short distance without disturbing the wiring, since any engineer who visits is not going to know how it was originally installed.