Im looking specifically at the Virgin and BA ab initio programmes and have a few months to prepare. Having spoken to a pilot at BA he recommended that I get a solo flight under my belt with perhaps 20 hours flight time too. Also a class 1 medical and ideally some time in a sim if possible. What about work experience? What about taking PPL theory exams?
You are probably aware that BA is not an MPL scheme but in any event, getting 20 hours under your belt and achieving solo is not necessarily going to benefit you - neither MPL or the traditional Integrated CPL course require previous experience and although demonstrating some interest, could be detrimental. As for PPL theory, unless you intend to obtain a PPL, studying at PPL theoretical knowledge level, although useful as background to further studies, would be largely a waste of time. You would be better prepared dipping into EASA ATPL level theory. A Class 1 is a good idea - making sure you can achieve the standard before commencing serious training is wise, although this will be also be taken care of by the training provider if accepted on a course. I wouldn't waste time playing in simulators at this level - you sound as if you need some structure to your plan. A PhD in Aerospace Engineering and background in investment banking - quite different fields, can only compliment your chances of success in achieving your goal and I would suggest searching these forums for further information and advice concerning integrated flying training and the MPL with respect to your two target airlines.
Best of luck!