hi matt,
First of all good luck with the course, I graduated in 2004 and know mech eng can be tough!
I have similar interests to you (currently doing a ppl course) and have pondered designing an aircraft myself. On the mech course you really dont learn enough about aerodynamics and aircraft systems to dive straight in. You do however learn the intricacies of mechanical design and have a brief introduction to fluid mechanics (an aerofoil section etc) so of course a little extra reading might get you in a position to give it a go.
Alas I dont know from a legal point of view if you are required to have any aero-related qualifications to design and build (CAA might not like it) but there is nothing to stop you getting said quals after your degree.
Once again, good luck, and when the going gets tough, head down the union bar
GW