The wire you described is the bonding wire and all continuously metallic piping must be bonded. Cold and hot water Waste water and gas. Remember the bonding requirement is for continuous metal piping. there is a lot of plastic in newer houses. Bond wires may terminate on the enclosure but not on the neutral block. that is for the ground wire which goes to an electrode.
The current ground rules will probably require a new electrode or electrodes depending on the type. Older services used 6 foot rods and newer grounds are to use 10 foot rods. Older electrodes are likely only a couple of feet long if they have been in the ground long enough to corrode. Older houses often used the water supply as the ground electrode. If the water service has not been chaged to plastic you may use it again but the local inspector may ask you to prove it.
Ground wires must terminate on the neutral block and may do bonding duty along the way. IE your ground wire can also bond the water, gas, waste and the service raceway bonding bushing along the way as long as it is not cut and spliced.
Thanks for your reply. This wire is not the bonding wire, nor are any gaslines or water lines bonded to ground. This wire is a #2 going from the main neutral connection in the fuse panel to a 1/2" cold water line.