Its when that rain occurs that is the crucial thing - that and the average temperature. You have a Mediterranean climate in Rome. As far as I can remember my old geography teacher once told me that a Mediterranean climate was the only climate that was actually dryer in the summer than it was in the winter. We have relatively wet summers that are a couple of degrees cooler than yours on average
Pretty much that. Rome is warmer with dry summer. It's a particularity of the Mediterranean climate. same hing goes for places like California, Chile and Perth Australia.
The thing is, it rains often in London but only small quantities with many cloudy days. Typical of an oceanic climate.