In the most formal of clothing lexicons, slip-on shoes are for wear about the house or with casual clothing outdoors in summer. Needless to say, that useage has gone out of fashion, and slip-on shoes are often worn with suits in the United States, Italy, and other countries other than England. The default style is arguably the Alden tassel moccasin, a perfectly fine shoe with an odd jacket but technically no better than a penny loafer under a suit.
The challenge with slip-ons is of course that their low cut decreases their formality and does not offer the support or protection from the elements of a laced shoe. But not all slip-ons are low sided. Bespoke shoe makers as well as a few of the better ready to wear firms such as Edward Green and Gaziano & Girling offer slip-on shoes that are the near equivalent of their laced brethren in terms of both form and function. That equivalency comes from higher sides than the casual slip-on, accompanied by elastic that allows them to be slid on and off of the foot for airport security.
Unlike low sided slip-ons, elastic sided designs like the George Cleverley bespoke sample in the photo usually feature enough brogueing to look somewhat like a laced dress shoe while preserving the slip-on's convenience. Every suit-wearing travelling man should have a pair, in my opinion.