BabyReindeer you won't like this but better to be forewarned.
In my over 25 years instructing on full-time/integrated ATPL courses you are very unlikely to have the time to do anything other than study for the ATPLs. It's the volume of sometimes pointless high class rubbish in the time required that is the killer. In addition to standard classroom time most students would probably spend at least 3 hours each evening and also some hours over the weekends (though I would always try to have a clear day).
ATPL theory requires 110% clear focus with no distractions or emotional baggage and you shall have to put your social life on hold for 6 months, a small price to pay in the long run. Students who ignore this advice are likely to be failing progress tests and the real exams with possible back-coursing or chopping. If you were fortunate enough to get selected I think BA (or any other sponsor) will take a poor view of you working part-time while they are paying for your training. Once you get to the flying phase things get more relevant and easier but you will still have to study about the aircraft & prepare for the next lesson.