Mech disc brakes creating too much slack I've got a 2nd hand bike to play with as I've never been into bikes. When I got it the brakes only stopped while I wasn't on it. I stripped the bike down for cleaning and I re-attached the brake cable but the right lever is creating too much slack. I've tried creating more tension by pulling the cable through the housing and then tightening the cable but on release it gives too much slack again.
Your actual rear brake looks like a electric scooter brake, I would ask whoever you got this bike from if they done any mods or maintenance on it. 

1st Image 

Unfortunately I don't think any form of adjustment will get you any sufficient braking.

2nd Image  

You can see from the second image the different cable route designed for use on a bike, generally the cable is fairly straight from the nipple to the clamp.

My suggestion is first find out if the brakes were replaced, and secondly if they were replaced which I suspect they're, you need to get the correct brakes installed for efficient and safe braking.

Artek Vigourous brake sets can be bought for £25 a set front and rear.