If the home hub lights are still changing colour when you get disconnected, then there must be an intermittent fault somewhere on the network.
I know you are using the test socket, but are there any other phone extensions that may have been incorrectly connected to the wrong side of the network?
Sometimes a line can come in via a connection block, and extensions have been added to this block, instead of coming from the master socket backplate.
Yes there are other sockets. I got a response from BT who confirmed a likely infrastructure fault so are sending an engineer today.
Hopefully they will find the cause.
Provided those other sockets are wired from the master socket, so that they become disconnected when you use the test socket, then the fault should be external.
Is quite common on older properties, to find that extensions have been wired to a terminal block before the master socket, and a fault on one of those, could show as a line fault, when its an internal wiring fault, and would be the responsibility of the home owner.
If all the extension become disconnected when you use the test socket, then that is fine.