I guess it could happen either way. It may be that when you register for their service that an 0870 number is assigned to your extension, however, most institutions that I have seen have the extensions already assigned to an 0870 number that relates in some way to the extension number but often not in an obvious way. In this case the room 0870 number remains constant if activated. It is likely just an assignment in groups to the physical location of the extensions. However the geographical number is often more closely related to the extension number (usually the last 3 or four digits are the same) Sometimes the first digit or two is only used internally to route an extension to extension call and these are replaced by part of the geographical code, sometimes not. But once one extension and its associated numbers are found similar numbers are relatively easy to deduce.
Sometimes the institution publishes an internal extension number and external number together eg for a porter's office in which case trying the same code can yield results if the internal number is similar to the one you require. Otherwise I guess we just have to work our way through all the registered area codes
You could try asking at one of the administration desks eg main reception or accomodation office if they can ring an extension for you to reach someone "whose internal number you know - but not their 0870 number" It might just show if it can be done across the unversity system and might reveal another part of the number.
Student Union might know if someone has already cracked the problem - there is often at least one practical joker on the union that lives to subvert the system and gathers such information. The price of a pint or a curry usually worked to find it out.