Just saw a TV ad for BT's anytime call package which includes 0845 and 0870 calls, and although I know this question is probably a few years behind current technology(!), it says it doesn't include dial-up internet access.

I'm sure there are still a few dial-up providers up there that allow 0845 dial-up, so do BT just have a list of these numbers or is it something smarter than that?

They know what numbers are from ISPs for dial up. Voice calls are inclusive, and data is chargeable. Its as simple as that.

From some sort of database..?

I think they have some sort of software which detects data calls as opposed to voice calls although I'm not 100% sure, but you can be sure they'll know!