The present invention relates to a new and distinct cultivar of Campanula plant, botanically known as Campanula×haylodgensis hort, commonly known as Bellflower, and hereinafter referred to by the name ‘PKMh04’. 
The new Campanula, ‘PKMh04’, is a product of a planned mutant selection and monitoring program conducted by the Inventor, Gert K. Jensen, in Søhus, Denmark.  The new Campanula originated from a mutation found in 2001 by the Inventor in a production batch of Campanula×haylodgensis ‘Marion Fischer’ (unpatented).  The Inventor selected the new Campanula cultivar on the basis of its sturdy, compact, and freely flowering habit.  Plants of the new Campanula are more upright, compact and more freely flowering than plants of ‘Marion Fischer’. 
Asexual reproduction of the new cultivar by terminal cuttings taken and propagated in Søhus, Denmark, has shown that the unique features of this new Campanula are stable and reproduce true to type in many successive generations.