Apparently the business started in the 1930's. According to Miller's granddaughter, her grandfather was the turner and Browne looked after the business side of things. She also said that he turned for Lawrie but did not recall him making bagpipes under the Miller Browne name.

There is a connection to Henry Starck however I'm not convinced we know the full story. According to Les Cowell (founder of David Naill Bagpipes and now deceased) "There was a firm in the east end called Miller Browne & Company that used to churn out loads of sets of bagpipes for various London names including Henry Potter & Co, Rose-Morris, and Boosey & Hawkes." If you look at a set stamped "Miller Browne" you might conclude that it was made by the Henry Starck company.
More significant evidence that Starck was the maker of Miller Browne bagpipes is the Brian Boru chanter seen at the left, stamped Miller Browne, London. Starck designed the chanter and owned the patent, and it is unlikely that he would allow someone else to manufacture it.
Miller Browne & Co.