you can do it yourself and it is a very easy DIY job (though testing is harder). 10mm Main Bonding cable is about half as thick as a pencil, and stranded copper under the Green & yellow. You can buy Earth Bonding Clamps (to go round the metal pipe) at the DIY shed, I would have thought about 50p if you just need one.
Verify that the cable goes back to the Main Earth Terminal which would be in or near the consumer unit. The G&Y should be a continuous length, with no cuts or joints that could come apart.
If the cable you discovered is plain (dark) green, and looks old, it might be old sink bonding which is not now required.
If you are not used to this, post some pics of the G&Y cables near the main fuse and Consumer Unit, and the cable near your water pipe.
It has to be bonded (within 600mm of) where the water main comes into the house, on the house side of the stop-cock.
the electrician ought to have connected and tested this and included it on his certificate, so it is a bit fishy that he did not do it. Have you paid him in full?