I'll dust off my memories of dial-up....ahem.
BT will connect to your ISP at 64kb at the local exchange or some other point back in their network. The data rate from the serving exchange will then suffer due to the line characteristics of the copper (or aluminium wire) between the exchange and your location. The internal phone wiring in your house will degrade the signal further (48k in my office, 34k in the dining room and even worse if it was raining).
The bottom line is that no ISP in their right mind has invested in dial-up since 2000 so the kit is getting a little tired plus contention ratios (available capacity to customer ratio) are probably 12:1 or worse as maintaining a network for cheap and cheerful services has no margin and the gold customers have since trotted off to limitless ADSL so in short, you are a Betamax customer in a HDVD world, expect crap.
I have experience of a few ISP's and can advise that most of the non-network providers such as Tesco, Wanadoo etc. use established carriers such as CWC, NTL/Telewest (aka virgin media smiling beardy git). They in turn are buying bandwidth off BT for some products so you pay your money, you get BT regardless ....unless you are on cable the god help you.
Change to ADSL while your dialup connection still allows you to order it online but when making a choice, ensure your tech support is free and if you ever need them, they have a brain and English as a first language.