Okay, recommendations:
"Serious degree" with flying content:
- Brunel University: Aviation Engineering with Pilot Studies
- University of Sheffield: Aerospace Engineering with Private Pilot Instruction
- University of Liverpool: Aerospace Engineering with Pilot Studies
- University of Salford: Aircraft Engineering with Pilot Studies
I have some knowledge of all of these - they are all serious degrees, delivered by dedicated staff, and the flying hasn't been allowed to dilute the engineering degree content.
If you really want to try and do ATPL at the same time, then use the long summer vacations to study ATPL theory with, for example, Bristol Groundschool, Cranfield Aviation Training School, or Bournemouth Centre for Flight Training. All are serious players with excellent material and won't cost much. If you work hard enough, this is possible - but will be tough.
Then for the further flying to CPL/fATPL - you'll have adequate time to do that after graduating from the academic course - work hard enough and you could just about do it before your student visa runs out. The UK has a great many schools very happy to do this flying training with you - most of them are pretty good, and browsing this forum will find discussion about most of them.
I may as well mention cost at the same time.
The degrees will cost you about £3k.pa if you are British or European, about £11k.pa if you are not, plus about another £6k for the flying.
CPL/ATPL groundschool will cost you about another £1k.
Living in the UK will cost you about £7k.pa
Hour building to be able to take your CPL course will cost you about £100/hr - so maybe £15k.
CPL/IR/Multi flying course costs will be about £16k according to the website of one flying school whose website I just checked.
So, if you want a real "grown-up" degree from the UK, AND a fATPL, then this will cost take about 4 years and cost you (assuming you're from outside the EU) about £78k.
As an interesting comparison, I think that the integrated fATPL costs will cost you slightly more than that, without living costs, and without the degree - although they will only take about half the time.
It should certainly produce a very capable person capable of working incredibly hard, and moving into a junior position then doing very well either as a pilot or aeronautical engineer very quickly.
But, you shouldn't underestimate the very substantial financial and workload commitment this would all entail. Nor how long it'll take to pay the debts back! You'd need to REALLY want this route.
G