The top half is the incoming connection into the house, this should only have 2 wires connected (and you're not meant to remove that part yourself, that's the telephone companies property and responsibility)
The bottom half is for connecting internal phone extensions. even if there is nothing connected to this part the main socket should still work.
Plug the phone into the test socket visible when you remove the bottom part of the master socket, if you are still getting no dial tone then it becomes the phone companies responsibility and you should call them out.
(welcome to the UK BTW)