Interest is simply rebadged as 'profit' or 'mark up' in Islamic finance.
I've got a current account, Visa card and car loan with Abu Dhabi Islamic Bank here in the UAE. 'Profit' charges are on a par with or lower than the interest I would pay with HSBC here in the UAE or back home, just packaged differently. However, I think it's the practice of Wonga charging mental interest rates that can seen as financially 'unislamic', with regards to the 'balance between moral and material requirement':
For example, my car belongs to ADIB until I pay the last installment. If I sell it, I have to clear the loan before I can get the registration changed to the new owner. A pain, maybe, but prevents recklessness from the feckless.
All in all, it's a lot more responsible and ethical than Wonga.