Just in case anyone following is having a similar issue: I finally got to the local phone repair shop, and he had a look around and has diagnosed a fault on the charging port, and it needs replacing.
I'd looked on youtube previously how to do this, and it's faffy, with heatguns for glue and plungers to separate the bits required. I have no idea of the cost of the part alone, but at just under £30 for him to supply and fit it seems like a bargain to me.