For AFTN you need a Telex or Sita connection, which needs a physical line (to form part of the legal confirmation process which Telex serves).
Telex is a dedicated link into the BT private network and costs about £50 a month (I think - I don't have me numbers in front of me).
Sita can be through either a leased line or a dialup connection. Though you have to be a member of Sita - and that means a bank guarantee and a lot of money!!
There are ways of getting around it - such as using Jeppesen to file them through your -pc (www.jetplan.com).
But if you want AFTN, the cheapest is Telex.