At a graduate level, there is a wide variety of roles available, and these are competitively fought for by applicants.
Summer internships are fast becoming the way by which banks recruit their new starters - after all it gives them an extended period of time to vet potential employees before they join. As such, if you are a current university student, it would be wise to consider the internship option should you wish to enter banking at a later stage.
Applying for more senior finance roles without a background in finance is much harder, and most roles require previous industry experience, though there are certain roles where a professional services background or MBA may be sufficient to negate the lack of experience.