Phone landline and internet doesn’t work at the same time

[Atlanticflyer]

Novice here, really confused. 
For the past 5 days my landline has not had a dialling tone and whenever someone calls they hear an engaged tone. For couple of days the internet keep dropping every 5-10 minutes, looking at the router I can clearly see the lights flash red and sequence through amber and eventually turn green. This now seems to have resolved but the difficulty with landline remains. 
I have changed the dsl filter and when doing this I forget to plug the modem back into the phone socket, instead the I plugged the filter with the phone attached into the phone socket and the difficulty with the dialling tone was resolved. However, as soon as I plug the modem and dsl filter into the phone socket the internet works but still no dialling tone. 
Any ideas what is happening or what I’m doing wrong?

[XRaySpeX]

Have you tried the phone & router in the hidden test socket?

[Atlanticflyer]

Many thanks for reply. The phone socket doesn’t have a split front panel. 

[Mustrum]

@Atlanticflyer  could you expand your explanation on what you do have? How many sockets, what type and so on.

It sounds like you have something wrong with either your phone or router or socket? Do you have any alternatives to try?

[XRaySpeX]

Show us an image of your phone socket.

[Atlanticflyer]

Here is an image of the phone socket. 

the main phone socket, plugged into the socket is a modem cable and a space to plug in the filter which had the phone cable plugged into it. 
many thanks. 

[Atlanticflyer]

Hi.  Thanks for your suggestions. 
the phone works ok, works when the filter is plugged directly into the phone socket and the modem cable is unplugged, it’s when they are all plugged in when it’s starts to fail. 
that the only socket and I only have this router. 

[Mustrum]

@Atlanticflyer   what happens when you remove that splitter/extension and plug the filter directly into the phone socket?

Also, is the other  Diamond socket connected to anything?

[XRaySpeX]

Dunno what's going on there.

1. What's behind the off-white splitter?
2. What's that loop of off-white cable seemingly going into it?
3. Where's the router DSL cable?
4. What's that "Diamond" box that looks remarkably like a master socket & why aren't you using it?

[Atlanticflyer]

If you remove the splitter we no longer have the internet but the phone works. 
diamond was there when I moved in, not connected to anything, I believe it was the box for cable tv