Whilst most banks will make some form of credit checks you can usually get a card for internet purchases such as a Visa Electron or Solo (Switch but less able to put you in debt) card.
The difference being most retailers, including those online, have a shop "floor limit" which means if you spend less than, typically, �50 the card terminal assumes you have the money in your account with switch and Visa Debit, but with Visa Electron and Switch Solo the terminal checks your account for every purchase therefore never allowing you to go into febt - these are very safe for banks / building societies so they'll give 99.9% of people one. Some retailers won't accept them but almost all will nowadays.
Basically, you'll be ok for an account and a card but in line with what you want you won't have the opportunity to get into debt.
Hope I was of help!!