I don't include tradespeople in this or one-man-band types. I mean shops and businesses on the high street.
I've been going to the same boutique for years and they've always requested that everyone pay cash. Same with a cafe I went to a while back. When I questioned them they say it's just how things are done. 
In this day and age with contactless, smartphone payments etc what legitimate reason would a business have in not permitting card payments?