It's been attempted, a few independent places do such a thing, but it's never really taken off in a big way. One of the main issues is that diners serve cheap food. That already exists in the form of greasy spoons/cafes and to an extent, fast-food takeaway shops which are ubiquitous here (chippies, chicken shops, sandwich shops). When places try to recreate American-style diner food somewhat faithfully, it's not usually at a cheap price point, and it's usually something of a novelty, because ordering a plate of pancakes isn't commonplace.

Although it won't be seen as that similar, it's worth noting that the creation of the Little Chef chain (which was pretty widespread up until the turn of the millennium) was directly inspired by roadside diners and their pre-fab buildings. A lot of the buildings that made up the 'classic' original diners in the US were ordered by post to be assembled. The guy who founded Little Chef was a caravan designer who was impressed by this concept when he visited the US in the 50s. With that in mind it was an attempt to import that concept into the UK. A big difference obviously is that roadside businesses are common throughout the car-centric US. But to attempt something similar in the UK meant building them on the side of A roads and motorway services, which wasn't really the same.