Mech disc brakes creating too much slack
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.