Stick with your first idea of a engineering / professional degree, just one which is more practical than heavy maths.
The employment rates for all the acredited courses have been in the 90's for years and most engineers don't acually work as engineers because of there problem solving training and managment/ accounts courses. They get employed in all sectors accounts through to IT although not many in personel deptments
.
In fact i believe that engineers have a higher rate of first time passes in Chartered Accountacy that accounts graduates.
And the old joke "What do you say to a arts graduate in there first job...." is unfortuntely in the experence of my friends very true unless they joined the forces or became Teachers.
MJ