Assay office and date are London 1807 so you were correctly informed. To my eye the maker’s initials are either BM or RM. There does not seem to have been a BM active in 1807 so I believe that this is the mark of Robert Makepeace. He was the son of another Robert Makepeace so he is normally referred to as Robert Makepeace II.
At this period (c1790 - c1820) it was not unusual for the town mark to be omitted from the hallmark. This is true not only for London but also for the other major assay offices so there is sometimes confusion over where items were hallmarked. In this case the shape of the date letter punch makes it a London piece.