After having taken the car back to the garage (thank goodness we got it with warranty aye) and have the friendly mechanics look at it they discovered that the muppet who had it before decided he’d try mounting an amp on each speaker. This is possible, but he’d screwed up royally and there was no sound at all.
The head unit worked, but no sound. So the mechanics ended up rewiring the whole system. This would have cost a few pennies to say the least.
They also fixed the ignition issue whereby the car wouldn’t start all the time – this was due to a loose connection to the switch or inside it. They took it apart and sorted that out too.
I can wholly recommend Graham Hilton Cars (Stevenage Road Garage Ltd.) – they’re service is fab. My Corsa, previously my parent’s car, also came from the garage.
Next steps… physical improvements. New MG Badges!