Fluffy bunny. Yes, they don't ask for I.D but they check your name and address to verify your identity, which you fill out, on the online application form. If you read the terms and conditions of these cards, it clearly points out you need to provide your correct information or they can report you to fraud departments, and even cancel your card. This is why you have a high limit of up to 5000 because they have already verified your identity by giving them your details (name / address). So they don't need to see you I.D, they ask for I.D if the details that you give them don't match up with credit agencies.
The IDT prime card you can buy it in-store has a yearly credit limit of ?300 per year and I assume other card that you can buy in store are also the same because they have to follow regulations that prevent fraud / money laundering. If you want that lifted you, have to go online and provide them with your name and address.