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All dial up services will be slow - you are limited to the 56kbps modem, which rarely achived even that. However even with an ntl phone line you should be able to use the majos=rity of different ISPs dail up services. I doubt there would be much financial advantage, and in many cases you might be penalised if ntl's phone service will not allow the special rate prepaid freephone dial up connection.
Realistically broadband is your beneficial option. There are only two main braadband technologies (excluding speial needs areas like satellite or local WiFi). Cable or ADSL. The cable systems are only available in the ntl or Telewest areas, whilst ADSL is available to the majority of people served by a BT phone line. You can't have an ADSL service without using a BT type phone line, although some ISPs (like Bulldog) now offer to take over the entire phone and broadband service as part of LLU (this might save costs but only apllies to a small area of the country at present).
ADSL has a wide choice of ISPs offering different price ranges, speeds and other levels of service. Cable is stuck with the ntl or Telewest service and price tarifs (you can only have ntl in a ntl area, and vice versa), although you can also get AOL over ntl cable.