[2013 - 2016] - Aircraft Engineering Course at University.
[2012 - 2013] - PPL Licence + Build Hours.
[2013 onwards] - CPL + IR, Then Build Hours.
[2016 - 2019 or whenever I finish ] Apply for an airline.
As pointed out, ATPL exams need to fit in somewhere. They are hard. You need at least 6 months full time study on them and they will not fit along side a degree.
Confused as to why you would build hours after CPL+IR, unless you mean keeping current. But building hours is only necessary before CPL. You'll need an MCC as well before applying to airlines.
I'm paying £60k for my modular, but that'll become £80k with the type rating needed. How much is the degree going to cost you?