You don't need work experience for either course, the benefit of work experience would be to gauge how you feel about that area as a career.
I'd note also you can go into finance careers from an engineering degree. In fact many finance careers (e.g. accountancy, investment banking, management consulting) you can go into with any degree - you could do Assyriology or evolutionary anthropology or marine biology. For the lBanking or consulting you'd need to go to a target uni ideally though.
In any event just do wider reading around your proposed subject area, see what kinds of related activities you can get involved in, and apply with that. That's all you really need at absolute most.