No need for apologies ..probly my grammarI may of misunderstood what you were saying. You appeared to be suggesting that OP strips 3” of insulation off the cable to the hob and twist the conductors of the new twin and earth cable (these conductors will be solid not stranded) to the existing cables and tape the cables together!
I don’t believe that @Fab Foodie is stupid enough to do that and I would be insulting him by suggesting he might think about it.
If I have misunderstood then I apologise. If I haven’t misunderstood then I suggest you delete it.
But just to help
The cooker cable is existing and will be used for a draw string ONLY
Tape 2 T&E cables staggered but neatly along a REPLACEMEMT cooker cable tape ends to form a smooth "ramp "
So that the existing cooker cable can effectively be used as a draw string the 3 solid cable be twisted together fir 3 or 4 "so as it does not come loose
Tape up this joint to remove any edges
Pull the existing cooker cable through toward the consumer unit and away from the concrete floor in kitchen
You will now have another cable for the cooker AND two T&E to join on to the ring main at the nearest accessible socket with tbe other 2 ends providing fir the new kitchen socket
The only bug bear being if tbe joists are tight holes and don't allow the 3 cables through ?
But if that's the case just pull it back and your back to square one