My main router is a Vigor2710n wireless unit. It has 4 wired LAN sockets.

I also have an old Vigor2600 wired router sitting spare.
Could the Vigor2600 be used as a network hub, which I can then attach to the Vigor2710n unit to increase the number of available wired sockets?

Yes it can but you must turn off the DHCP server on it otherwise it'll fight with your Vigor2710.
I think it's 10/100 speed only.

Interesting, thanks for the info.
I assume it doesn't matter which 2600 socket is used as the feed to/from the 2710n. I can experiment later.

I've used one as a hub, just turn off DHCP as others have mentioned and check the management IP address doesn't clash with anything on your current sub net. Doesnt matter which port you use (from memory) as they all just act as a hub (possibly switch, not too sure).