JJMcVitieIt seems it's fairly common that a solder point breaks loose. It's a simple fix if you got a soldering iron and helps if you got the solder too but you might get by without the solder. I think I watched this video to get at the wire. https://www.youtube.com/watch?v=6HYH6zJ9sVM&t=82s.
for the most part open it up and look for the wire that's barely hanging on and touch the hot iron to it for a second to two. i wouldn't recommend it but you could even try just tapping the loose wire into position as well. just need it to be firmly touching the solder joint.
Michael-QHey Michael, I finally got around to buying a soldering iron and solder, and following the video you sent made repairing my headphones 100x easier. Annoyingly the white wire was loose down in the actual speaker housing so that made things fiddly but it all worked out in the end. Cheers for the video!