The first thing to do is go to the master socket and, as long as it is the correct type, remove the lower section of the faceplate to reveal the test socket behind it.
Plug a phone and nothing else, not even a filter, into that socket. If you do not get dial tone on that socket then chances are the fault is external to you as the test socket is wired directly across the incomming line. And removing the faceplate disconnects all your internal wiring.
If however you get dial tone on the test socket then the fault is internal to your home.
So first of all put the faceplate back on. Plug the phone without the filter or router into the socket on the front of the master socket. If you get dial tone then the filter may be faulty. So try using the filter with just the phone connected, no router. If no dial tone throw the filter away and get a new one.
If you get dial tone then plug the router in. If that kills the dial tone then the router may be faulty or miswired. As with the Sky box you can accidentally plug the phone line into an ethernet port with the same effect.
If you didn't get dial tone just plugging the phone on it's own into the master socket then the problem could be an extension, either something plugged in or the cabling. So first off unplug everything that is plugged into an extension socket. Test the master socket again. If there is dial tone then go round and plug each device back in one at a time and test each time until dial tone dies. Whatever you last plugged in is likely causing the fault.
If there is still no dial tone with everything unplugged then there could be a cable issue. So you need to wander round chasing the cables and looking for signs of damage.
It can be a long winded exercise tracing a fault. If you're lucky it will be the incomming line which is your service provider's problem to get sorted. If however the fault is with your internal wiring and you called out an engineer to fix the line then very likely you would be hit with a call out charge and if the guy they send is a jobsworth he might well just turn round and say "not my problem mate" and bu**er off leaving you with a dead phone still. So if nothing else you should do the master socket test socket test (if that makes sense
) if for no other reason than avoiding a 100 quid plus call out charge!