I've never had anything from hotels in the mail.
Neither have I. I have however had an email from each one afterwards asking me to fill out a survey of how I felt my stay was but nothing in the physical post from any.
I have used Premier Inn, twice - (two different ones), Travelodge, Three times, (two different ones), and Whites Hotel. So you can be safe booking with any of them.
If you are worried about using a card. You can get a pay as you go credit card to pay for it.