Ev0lutionz

Using v brakes on my foldie, I undid the brake nut and the cable went into the housing, tried pushing it with a little force but to no avail, when I pulled it all out and then tried putting it back to the housing, realised I have frayed the ends and I do not have any spare cable and now I have to go to a LBS..

sweeks

A new cable will not have frayed ends, so you will be able to (carefully) insert it into the housing. If there is any doubt about the condition of the housing, replace that as well.
Some helpful links:
Sheldon Brown

cxwrench

I think you've figured out the 'tip' to replacing cables...replace them, don't re-install them.

frogman

If you have enough cable, you can cut it about 1/2" shorter, back where it isn't frayed, and squrt some super glue on the end and then you can push it through. But since you said it is too short as sweeks said a new cable would be the ticket. I aways do the super glue thing anyway.

dsbrantjr

It is also helpful to twist the cable in the direction which tightens the lay while inserting it into the housing. I use die-drawn stainless inner and lined outer cables. I see little/no advantage and much downside to the coated inners. I use Shimano or Jagwire for consistent quality but there are lots of varying quality and price selections. Buy an extra, they are cheap. Good information here: https://www.sheldonbrown.com/cables.html

veganbikes

Get new cables and housing and don't muck about with old used stuff. The only time I would try to reuse cables and housing is if they are brand new either unridden or very few miles but if frayed it is done. However if again things are new then I might swap that rear over to the front and cut off the frayed part but not used stuff.

Lazyass

A tip to prevent cables from fraying in the future: After you cut them to length and before you install the end cap, put a drop of super glue on it.

ThermionicScott 

While you're in the bike shop, buy a couple of brake cables. That'll save you a trip if you mess up the next one (happens to the best of us...)

dreamy

If you have a soldering iron a bit of solder will do the trick, buy may need to do a clean cut first.

But always have a few spares on hand as well

MNebiker

I always install new cables full length and cut them only after they are completely connected and adjusted. Saves measuring, the tips are usually sealed so no fraying to deal with - and eliminates embarrassing mistakes.

ThermionicScott 

I've tried soldering the ends, it's never worked well for me with stainless steel cables.

Crankycrank

Twist weld your cable ends. A little anal but I do it and permanently fuses the wires together so no need for anything else.

MudPie

For stainless cables, you might have to use a solder with a silver content, at least that's the only way I can solder stainless cables.

Regular solder works fine with non-stainless cables.

But overall, a soldered cable end is nice.