I think it's a combination of factors
-as pointed out above, an engineering mistake can kill a whole plane/train of people, so you want to know that the people designing and building are well qualified.
- engineers are very employable, and are well regarded (pay/status) internationally, even if less so in the UK
- competition, UK engineering degrees are sought after by many international students
- finance careers, engineers are sought by city companies as they have high level maths skills and interdisciplinaryworking experience
- cost of running the degree. I've read that engineering degrees typically cost more than the £9k fee charged. There's more lectures, labs, and assignments than just about any other course. And is typically on a par with the workload of the medics. So the uni will try to choose applicants that are self starters and will cope with the demands of the course. Good A level results is seen as an indicator of that.