Hi and welcome.

I take it that the volume control actually works and that you do get a reduction in level as you turn it down?

Assuming that, it sounds more like either a high resistance solder joint or a bad guitar cable. Hopefully you aren't using the guitar lead that came with the kit, as they are awful and should be thrown straight in the bin. The outer braid on them is a few whispers of wire with big gaps in between them and provides very little shielding for the signal wire in the middle.

Passive guitar pickups make a high impedance circuit and high impedance circuits are prone to picking up far more noise than low impedance circuits. So anything that increases the circuit impedance, such as a poor solder joint, increases the system impedance and makes it more prone to picking up noise.

With the volume knob at 10, you've got maximum output signal, so the best signal/noise ratio. With the volume set to 0, the output signal is grounded so any noise is also grounded, hence no noise. But with some dodgy connection and a lower signal output, you will be prone to more noise.

It's highly probably that one of the pickups is 'reverse wound/reverse polarity' (RWRP) with respect to the other (the magnet's polarity is flipped and the signal is sent the other way around the coil). This isn't always the case with pairs of single coil pickups, but it would explain the lower noise level with both pickups. With one pickup being RWRP, its signal output ends up being the same polarity as the other pickup, but any noise picked up is reverse polarity with respect to the other pickup, so the two noise signals cancel each other out to a large extent. You effectively create a humbucker pickup with widely spaced coils (but with the coils wired in parallel as opposed to the standard series coil connection of a humbucker so the sound is thinner).

So you need to track down what is probably a poor ground connection. Have you got a multimeter? If so, check the ground connections from the output jack back to all the ground connections on the TL wiring e.g. backs of pots and the control plate. resistance should basically be as low as your meter measures with the probes shorted.

If not, you could start out by simply redoing all the solder connections.

Posting some pictures of the wiring and shielding will help us to see if anything obvious is amiss. I know its partly pre-wired at the factory, but they don't always get it right.