Well, technically you want to use the TalkTalk as AP. Range extenders typically connect to the network witlessly, while in your case you will effectively interconnect the routers by LAN. There are different types of power-line kits, but a basic kit of 2 with 2 routers, it would be as if you are connecting bother routers by an Ethernet cable.
I don't know how far apart the 2 routers. For a small apartment, you could in theory connect the router wirelessly, but that's subject to firmware, chip sets and drivers etc. So it's probably easier to just use the powerline thing, but I am just mentioning the other option if you want to try it first. A factor would also would be weather you care if the clients of the "extender" are on a different subnet or not.
Note that for Powerline kits, some have devices with built-in AP function (so you could just get rid of the TalkTalk router if you have no other reason for using it. It's worth looking at what's available in the market and check your budget.