Quick update on the situation / little DIY project!
Turns out that a surge protection extension lead I bought many years ago had many little nifty wires and connections with it.
These connections being the aforementioned coaxial to aerial converters.
I've got an aerial lead connected up to the coaxial now. Just awaiting a 3 way splitter for splitting the roof aerial upstairs then it should all be connected just fine.
Turns out keeping odd pieces isn't simply junk but rather useful
Edit:
Picture of the aerial to coaxial.
Ignore the ethernet spindle as that was in the same draw