A data extension kit. Or a length of CW1308 cable and either an RJ11 socket if you only want broadband at the new location or a phone socket and filter if you want telephony as well.
Even simpler, just disconnect the existing master socket, move it to the new location run the CW1308 between old and new location and join to the existing wires using a junction box and re-connect master socket.
A double socket, hub and phone connections
You did not specify which type of master socket you had, as that is important.
If I read it right, you said you had one of these
Is that correct?
Yes that's the one
Your options are somewhat limited unless you can run separate data and phone extension cables, as you seem to want a phone connection as well.
You could use a cordless phone, and leave the base station plugged into the master socket. Then plug an RJ11 data extension cable into the broadband socket at the top, and run it to the home hub.
The other option would be to remove the bottom section, and plug a normal phone extension cable in the test socket behind. Then plug a microfilter into the other end of the extension, and plug the phone and the home hub into it.
Is there any reason why you want to move the home hub, as you are likely to lose connection speed over a normal phone extension lead?
If its only a short distance, then it should be fine.
If its just a connection issue, then it would be easier to run an Ethernet cable from the home hub to your equipment across the room.
Message 4 provides the simplest option.
You don't need to run separate phone and data cables to the extension, just an unfiltered feed from the data extension terminals and use a filter at the extension. Not elegant, but straightforward.