@Jojoe if your conservatory has a dwarf wall the chances are they are in the cavity of the wall, if the interior of the wall is brick, as is the norm by sparkies and indeed me when builders have asked me to first and second fix. If the conservatory is plastered, dot and dabbed to the floor the cables are more than likely behind this as per normal wiring you have in your house. If you look at the wall of your conservatory in relation to your kitchen, the closest socket to that point is probably where they took the supply from as either a spur or carried on the ring. If you have undercounter socket/s for a washing machine ect and a swiched fused spur or gridswitch above to turn on/off undercounter sockets, it likely they have taken the supply from a undecounter socket, as its easier, less work tut tut! Switch the fuesd spur/spurs off one at a time to any undercounter soctet and see if this kills your conservatory. If this is the case you will see one grey cable coming down from the fuesed spur above the counter and another branching off to the side or downwards, which will be your conservatory feed. You may even see patch repair where they have run the cable. ?
It does have a small wall, think you are right I’m certain it comes from power socket on the other side of the wall. I’ll get an electrician to do it when I get round to taking the conservatory down.
Cheers
Enyaq EV