Give ntl: a ring or goto ntlworld.com stick your postcode in and you'll see if you can get broadband.
£14.99 a month for 128K cable modem connection which is cheaper than BT openworld 56K dialup.
Use it 24/7 365 days a year. Thats all it costs.
Plus you can get rid of your second line. £11 or whatever bt charge you.
£29.99 for 600K connection.
Use the onboard ethernet in your Amiga One straight into your cable modem. If the OS4 stack is anything like miami three clicks and 1 press of the return key and you'll be setup.
Its so easy to use an amiga with a cable modem.