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Noob2013
Walk away
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Discuss Routing problems in the Electrical Wiring, Theories and Regulations area at ElectriciansForums.net
Get a quote from a groundworks contractor to dig a trench and lay in a duct, leaving you to do the easy bit. Then it's up to the customer to accept the price or not.
1 you don't run cables along listed walls.
Hense the post asking for alternatives.
2 with a digger.
Won't cutting through the roots of a 100+ year oak or other large trees undermine it and risk bringing it down?
3 find and fix the fault on the existing installation before adding anything new to it.
I have investigated a bit and found the garage circuit is tripping due to an old fluorescent light. This can be replaced. I have identified another cable on a kitchen fused spur that runs via two external bulkheads to the existing tree light, and turning this fused spur on sends power down the cable to the tree light and trips the kitchen RCD after about 10 seconds. Disconnecting this circuit at the last joint before the cable enters the ground towards the tree cures the tripping, and the existing cable entering the ground is very old and has visibly determinate.
Walk away 
solar lights?
Reply to Routing problems in the Electrical Wiring, Theories and Regulations area at ElectriciansForums.net