Investment banking, professional services, actuarial, management consultancy, civil service, IT companies are just some you could pick from. Honestly, experience matters more than anything so if you have something to genuinely talk about in the "Tell me about a time when..." interview questions, then that really makes a difference.
I have in the past been given offers from and/or worked for the Big 4, an investment bank in NYC, an educational charity and various smaller jobs e.g. summer schools, tutoring.
I'd recommend the Graduate Area Manager for Aldi job if you want to sell yourself, have no life and hardly any sleep. Then again, people only do it for 2-3 years before they burn out and get replaced don't they, that's the point in the scheme.