That is terrible. I would strip that crap back and start fresh, looks a right mess...
If you cannot solder these then take it to someone who can, audio wires CAN be soldered so don't listen to people here, you have to know how to do it.
It's an easy job to do professionally, if it was me I would use 3 peices of heatshrink and solder the 3 connections (cover in heatshrink after) and have a larger peice of heatshrink to put over the top of the 3 connections.
You not got a friend who can do it? P.S. Where in London are you?