Perhaps someone left a laptop at the exchange MDF for casual browsing and downloading
The thing with BT Click is that it is just a 0845 number that can be accessed from any PSTN line with no ISP membership required. This is an advantage for when your away from home etc but also allows the potential for abuse.
I agree that it was likely a billing error, especially with 80 call set ups, but you never know...
Unfortunately call set up is the most expensive part, 5p or something followed by local rate (1p or 2p per minute?).