1) Economics, although engineering jobs are available and an engineering degree is still allowed for economics related jobs like investment banking and accounting, which are mainly located in the financial districts of London (City and Canary Wharf)
2) probably economics since lse and ucl both are highly regarded for economics but imperial is highly regarded for engineering and is one of the best in the world for engineering.
3) economics leads to a wide variety of careers, as does engineering. A lot of the jobs that you can get with an economics degree are also available with an engineering degree, such as investment banking, which has very high salaries and extremely long hours and high competition.
Overall, both degree subjects would be good for the 3 criteria you specified.