I'm a little late to this topic and found it by accident while doing some research on a tenuously related topic.
All electronic equipment has the potential to cause radio interference, including various types of routers. As your neighbour is a CB user he has little in the way of any legal recourse. CB radio was deregulated in the 90's, meaning users were no longer required to purchase a license to use the service, and as a result were no longer considered a protected service. I doubt OFCOM will be interested in following up his complaint and will likely close the case without any investigation.
A common source of interference to the CB bands that is internet related is the emissions from HomePlug devices, the devices that some use to increase the range of their network by passing ethernet over the mains wiring. These are essentially radio transceivers operating on the Shortwave and VHF frequencies. Because house wiring is unshielded and unbalanced the energy from these devices is free to radiate, and can radiate quite a distance. All devices sold today have to be prevented from radiating in the primary amateur radio allocations and those used by essential services, CB radio is not classed as either and therefore no restrictions on emissions on those frequencies are in place. It's also worth noting that a very large amount of digital electronic equipment use oscillators running at 13.560MHz, the second harmonic of which is 27.120MHz, which is withing the CEPT CB allocation.
As others have stated the onus is not on you to fix the problem as you are using the equipment supplied by your ISP as intended. One thing your neighbour needs to do is determine by which method the interference is getting into his equipment. This means is it coming via his antenna? Is it being picked up by the shield of the coax he is using (known as common mode interference)? If it's coming via his antenna then repositioning his antenna may reduce the effect. If it's coming in via his coax shielding then a common mode filter or line isolator may reduce the interference. It could even be mains borne and therefore mains filters may help.
I do have sympathy with your neighbour but to make accusations from the start is not the way to go about things and often leads to unwanted tensions between neighbours. I'm a licensed radio amateur and I live in a typical suburban environment. Consequently I am surrounded by a multitude of unwanted sources of interference. These range from cheap phone chargers, battery chargers, inverters used in Solar installations, VDSL leakage from overhead telephone cables, switch mode power supplies used in set top boxes (Sky, Virgin Media, EE, etc), in fact anything electronic can cause unwanted interference. Rather than waste my time knocking on everyone's door insisting they turn everything off I have tried my best to adapt to the environment. This has included carefully choosing the type of antennas I use and their locations on my property. I have also built some heavy duty mains filtering to ensure there is no noise from other properties getting into my property.
Have all my preventative measures ensured that I'm free from locally generated radio interference? No, but it's a compromise. I have a license to do what I do and I'm fully entitled to do what I do. But by the same token my neighbours have bought their electronic gadgets in good faith and are using them as intended and are free to do so. If anyone is to blame it is the manufacturers for not applying the appropriate filtering, and the regulatory bodies for not enforcing their own requirements.
