Is the "network rubbish" LAN or WAN traffic? If it's LAN and the devices are wired get a cheap unmanaged Ethernet switch, plug that in to the router and all wired devices in to the switch - that will take the traffic away from the router.
Thank you for that very sensible and elightening advice. All I can say is "doh!", that hadn't occurred to me.
I've ordered that switch, and will give it a try with my old router (which I like much more than my new, expensive, crazily-feature-larded one).