Mydaea corni
There are quite a number of Mydaea species and most are very hard to identify. Luckily Mydaea corni is not one of those. The shield or scutellum is entirely brown. In most other House Flies it is grey, black or partly brown only. The scutellum is the backwards pointing triangular last part of the thorax. In the picture it is clearly visible between the beginning of the wings. The larvae of Mydaea corni live in funghi, especially in Milk-caps (Lactarius species) and Russulas (Russula species).
This species is also known by its former scientific name Mydaea scutellaris.