I do not understand the science behind it all but the time it takes for them (any and all I suspect) to release the assigned IP and allocate another varies considerably.
I'm with BT and sometimes its 10 minutes, sometimes 40.
If quick changes are important then you're better off with a mobile sim or mifi dongle.
The reason it's important as sometimes I forget to disconnect the ethernet cable from my PC when I plug in my usb modem. So I don't want to log into my stealth accounts with my real IP obviously.