Anyone who doesn't understand what's so difficult should read this:
https://wiki.c2.com/?WhyIsPayrollHard
Its from a different domain, but it gives you a flavour of the headaches you encounter. These systems always look simple from the outside, but once you get inside you find endless reams of interrelated and arbitrary business rules that have accumulated. There is probably no complete specification (unless you count the accumulated legal, regulatory and procedural history of the DVLA), and the old code will have little or no accurate documentation (if you are lucky there will be comments).