How do I get plans for pipes and cables going under the property garden?

System

There's a very slight chance drawings of below ground utility/drainage runs will have any relation to what's actually in the ground... (Outside of main sewers etc under roads or pavements)
Better just to dig what you need to, carefully and see what's there.

JP1978

Maybe ask more builders for quotes, they may take a different approach - ie, hand dig after doing a cat scan - maybe the builders you have now want to take in a mini digger?

A hand dig is unlikely to penetrate any ducts or cables - assuming that they have scanned the area first.

parking_question_chap

You will need to ask the utilities providers in your area.

Furts

Is OP's builder competent? Is this builder a cowboy? We cannot say but what can be said is a competent builder would use a CAT and a Genny, they would also trace drains, and they would hand dig trial holes around the perimeter, with a non conducting spade. None of this is rocket science, it is simply everyday common sense. The fact that all this appears to have been ignored and instead thrown back at OP is deeply worrying.

r_sole is spot on and to add further to this, any drawings are worth less than the paper they are written on. Nobody relies on drawings of services to be accurate, or comprehensive. Nobody that is except cowboys and bodgers!

sooty&sweep

Hi
Someone I was talking to recently said he'd had problems with hitting a utility pipe, can't remember which one.
He'd been digging in a flower bed at no real depth when he hit it with his spade
Apparently they'd used a boring machine to put the pipe in. If the machine hits something in it's way it'll go over or under it. In his case over it so the pipe wasn't very deep.
They tried to charge him for the repair but when he pointed out it wasn't at a safe depth because of how they'd installed it they left him alone.
The utility companies might be able to tell you what depth the pipes should be at but that doesn't mean they will be at that depth.

Jen