Looks like a lot of extra unshielded wire in there which could be acting like an antenna picking up electromagnetic interference. I'd get rid of that and just use the shielded wire from the pickup. Also you should ground your bridge so the strings don't also act as an antenna.
Ok, thank you for your response, will give it a go. When grounding the bridge, connect from the bridge to anywhere on the guitar or into the wooden body.
Normally you ground to the back of a volume pot but I don't see one so I assume you don't have one, in which case ground to your output jack.
I see what looks like 3 wires coming out of the pickup, which looks like a hummbucker, 2 wires joined together as 'ground/earth'
You might be shorting the second coil to ground by connecting the ground and the 2nd wire together.
unsolder the wires and use a multimeter to check the resistance (ohms) between each of the wires from the pickup and report back...