One person who advocates this position is Andrew Gregory (The Reception of Luke and Acts in the Period Before Irenaeus, page 2), who says that the modern assumption of Luke and Acts as two volumes of a longer work is a modern construct. He says that this is not to deny that Luke wrote two successive volumes and possibly set out to write two successive volumes, each of which largely coheres with and informs the other. He simply notes that for much of their subsequent history the two volumes have not been read in this way. Although Irenaeus made use of Luke and Acts together, it would appear that this was not typical.
To add to Gregory's position, if Luke and Acts were intended to be read together, then it can be expected that they would have been circulated together. Our earliest manuscript of Luke's Gospel is P75, which contains about half of Luke and John, but nothing of Acts. The third-century manuscript known as P45 shows the gospels in 'Western order', with Luke separated from Acts by Mark.
Mikeal Parsons and Richard I Pervo (Rethinking the Unity of Luke and Acts) argue that singular authorship of Luke and Acts (which they accept) does not automatically imply generic, narrative, and theological 'unity.' They say (page 1) Luke and Acts served different purposes in early patristic argumentation and exposition.
While Raimo Hakola ('"Friendly" Pharisees and Social Identity in Acts', published in Contemporary Studies in Acts, edited by Thomas E. Phillips) does not consciously discuss the separation of Luke and Acts, he discusses at length the different treatment of the Pharisees, in Luke and Acts. Hakola says that while Luke is negative towards the Pharisees, Acts is quite positive to them. One could expect that if the author wrote a two-volume work close in time, intending them to be read as a whole, then he would treat such an important theme consistently. The conclusion to be drawn is that when beginning to write the second book, our author had already moved on from some of his earlier theological assumptions and was making a fresh start. In any case, if modern scholars read the two books as merely two volumes of a combined work, they must run the risk of reading the theme of one book into the other.