Your employer seems to be adopting a 'belt and braces' approach to ensuring that they comply with the legislation.
The law isn't based upon the usual principle that they can't be successfully be prosecuted unless there's clear evidence to show that they've employed illegal immigrants. Instead, it requires employers to be able to prove that they've not done so. In order to prove that all of their employees are 'legal', employers must ensure that they've seen a relevant document from the 'specified list'. Your passport is one such document but your P45 from your previous employer (showing your National Insurance number), which they presumably had many years ago, would also suffice (as would your birth certificate):
http://www.ukimmigration.com/employer/uk_work_ permit14.htm
Chris