Do you use or need ADSL broadband over your telephone line? If not, then just about any type of telephone cable can be used to run to an ordinary extension socket.
There are 4, 6 or 8 wire cables available. A standard telephone socket only really needs 3 wires.
If you do use ADSL, then you will need to fit a filter on the new socket, or fit a socket incorporating a filter. Multiple telephone sockets are probably best 'daisy chained' one after the other instead of wired in a 'star' from one central point to reduce unwanted ADSL signal reflections, which can limit connection speed.
There are higher specification cables available (eg Cat 5), which may give better results if you are using ADSL, but the system is designed to use ordinary telephone cabling.
If wiring is to run outside it may be better (but not essential) to use black or brown sheathed cable, as this is less susceptible to degradation from UV light (direct sunlight), and may blend in better with your walls.
You could install this yourself or ask BT etc. to install a new extension socket for you. The basic socket wiring is the same wether you use ADSL or not.
There is a limit to the number of telephones, modems etc. that can be installed on a standard line. Each device has a REN number, usually marked on it. Sometimes it's very low eg. 0.1, or it may be as high as 3. The total of all the REN numbers connected should not exceed 4.