Easily replacing cable

I need to replace a telephone cable (consumer side of master box). I think the old cable has broken strands inside it, but the outer insulation is fine. The cable takes a slightly tricky route through stud wall. What I'd like to do is securely fasten new cable to the end of the old cable, and literally pull it through, so it follows the original cabling route.

What is the best way to secure the new cable to the end of the old cable, so it does not come off half way through the wall? Whatever method is used, it could not be larger diameter than the cable itself (because I do not know whether the holes the cable has to pass through are much bigger in diameter than the cable itself).

Thanks in advance

Ed

I would advise you to test if there are actually broken strands in the cable before going to the trouble of replacing it

Thanks Martin. My tests suggest that there definitely are.

I think the cable got stretched to breaking point when we moved the position of the socket a little too far... But the outer insulation looks to be in tact - if I pull the cable, the other end moves freely.

Use the old to pull through something strong like a high strength fishing line.
This is narrow in diameter and strong. Using Tallow on the free end to help it glide through
Once this is through attach your new cable at the other end. Use some Tallow again on the new cable as you drag it through ( carefully).

Job done.

And gentle pulls not hard tugs, if it gets stuck feed back try again.