It might be unusal for them to have dedicated parking facilities (though there are a good number of Starbucks and Costa drive thrus now) but outside of London and city centres there is almost always shared parking close by.

I'm in the UK too, and I've found there are separate coffee shops that are focused on pedestrians vs car users. The first are your typical shops on the high street (which yes you could park near to but that's not really the focus) while the second are in motorway services or in a retail park built around a car park (what Americans would call a "strip mall"). If you're a regular user of either one then it's quite easy to imagine the other doesn't exist but actually they're both very common.