The modern telephone system is still mainly  using analogue lines to connect homes to the nearest telephone exchange.

 However, BT have been working steadily on a program to convert all of their exchanges from analogue to digital, however, this is still work in progress. 

If you are connecting to the internet with a 58Kb modem then you are still using the analogue telephone system.

During the 1980s, a new technology called ISDN or Integrated Services Digital Network was developed by BT. 

It was prohibitively expensive so only businesses could initially afford it.  As with all new technology, prices eventually fell and the cost of this technology is now within reach of homeowners.

For domestic users the BT ISDN service is called 'Home Highway'

An analogue modem allows speeds up to 56 kilobits per second. But ISDN technology allows speeds of up to 128 kilobits per second.