Lactococcal bacteriophages can cause fermentation failures in the cheese production (e.g., Cheddar), especially when the by-product whey (≤109 plaque-forming units mL−1 of bacteriophages) is recycled and added to new batches. Using membrane filtration, the bacteriophage titre in whey can be reduced by 4 log units without protein denaturation. To achieve higher bacteriophage reduction (≥9 log units), we attempted an orthogonal process strategy (combination of different technologies supporting each other). Three representative bacteriophages were inactivated in membrane filtered whey by (i) UV-C irradiation and (ii) heat treatment to achieve additional 5 log units reduction. Thermal treatment was only partially successful, as the varying degrees of heat resistance required, in the worst-case, temperature-time combinations above pasteurisation conditions. In contrast, UV-C treatment required doses of maximally 2.25 J cm−2 for successful inactivation, thus representing a promising avenue for the establishment of a novel process for the production of “phage-free” whey.