As discovered, Clockwork and P7 are quite easy to tell apart, since the P7 is a bigger tubed beast, that was its 'selling point' BiTD.
(assuming clockwork era most people think of, being early 90's)
The serial number should give you the year of the frame with the help of the people above, it may even give you the model. I don't know.
Clockwork and Prestige would probably need photos along with the serial. The weight of the frame may also help. (again assuming the early 90's and not the modern named Prestige/Clockworks)
As for the C16x etc to P7 I have no idea, not something that has interested me yet.
<grumpy> This is not a 'sticky' sort of thread, but the sort of thing like many others that should end up in the Bike FAQ's also it's Chat not Readers bikes</grumpy>