Hi Martin
The speed you receive is governed by a number of issues. The most important of these is the distance you are from the exchange and the quality of the line (thick copper, thin copper, aluminium etc). That will determine your attenuation, which in turn determines the fastest speed at which you can connect. Your router or modem should be able to give you that information.
There is a second factor which then kicks in, and that is the IP profile. To save themselves some computing power, BT impose a profiling system which restricts throughput to a figure lower than the connection (or sync) speed. In addition, their profiles have 500k increments, so a change in sync speed of just 32k can move you up or down by 500k. Important when using a modem.
The final factors are the possibility of congestion at the exchange or within the ISPs network. This will usually be seen as a slowing of throughput at peak times.
If you move to an LLU provider offering ADSL2+, you should see some speed improvement, but you will not get 24Mbps unless you are currently synching at 8128. At a rough guess, you'd probably see 6-8Mbps, but if you can post your current sync speed, noise margin and attenuation, I can give you a better estimate.
I would always recommends using a router rather than a modem, it's far more secure and likely to give better results with rate adaptive services.
HTH