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That is indeed how it should work. Are you sure you are connecting to the right Ethernet wall plate socket? Have a look at the 'After' picture in this thread post 55 https://community.bt.com/t5/Connected-Devices-Other/Can-I-use-separate-modem-with-new-BT-Smart-Hub/t... to extend your DSL line via the Ethernet cables using RJ11-RJ45 patch leads.
My first though were 'am I connecting it correctly?' So I checked all 6 Ethernet sockets on the wall plate and none work. Also the lights on the router don't light up next to where you insert the Ethernet cable.
What have you got connected at the other end?
I also have a plugged Ethernet for a youview box and that lights up and works fine. (Hope that makes sense).
Not sure what you mean by this.
If the youview box works OK via the Ethernet links, then it would appear the problem lies with whatever the other device is or the link that goes to the other device is faulty. I assume there are 6 sockets in the utility room that go to 6 different rooms in the house. Try the other device on the same link that the youview box works on, if it works then the problem is with the Ethernet link. If it doesn't, the problem is with the device.
Ok, posts crossed. Youview box is not using the Ethernet links. I think you need to get a tester to check the connectivity of the Ethernet links.