Various people are correct here.
The cable does need to be replaced, could have drilled through power socket, and turned a ring mains into 2 radial circuits.
(which is a big difference). Possibility that the insulation has been completely damaged and the cable is quite happily arcing away
underneath the plaster.
You need to either replace the whole run of that cable or junction box it, but must have the junction box in the loftspace/floorspace above the cable and below the damaged cable, so that you can acces it. a sunken JB in the wall itself is unacceptable.
if it's a stud partition wall, you maybe lucky and able to pull teh cable out, with the new one attached to it, otherwise if it's
a brickwall, you'll need to chase all the plaster awayabove the cable for the length of the run on the cable.
you need to
1, switch all power off.
2, get into the roofspace or open the floorboards directly above where the cable is and locate it.
you Failed to mention if there was a socket or lightswitch in line with the big bang location.
If there is, it's a good guess that the cable in the socket/switch is traveling up the wall and you;ve located the top part of it.
get a replacement cable of same size and type, mechanically attach hte two cables together by tying knots with the strands of copper,
cover the joint in tape and put a load of washing up liquid on the new cable.
Hopefully if you pull on the cable at the top of the roofspace/floorspace, you'll pull the old and damaged one up, which will
drag up the new one up .
using the connector box, cut of the damamaged part of the cable and join the two cables together!
if there is no socket or switch, then the cable needs to be replaced top and bottom using two joint boxes.
open the floorboards up where you were standing and drilling, find the cable going up, cut cable, join new cable to it, as above,
and pull out the old one and hopefully drag up the new one. Now you will have to jointbox both ends of the cable.
by now, it's probably worth getting an electrician in unless you are use to DIY! a sparkie would have it fixed in an hour, it's going to
take you a few hours and a constantly worry about the quality of your terminations skills with the joint boxes!
Hope that helps