The distance from London to Rome is only 1157 miles. If the messengers rested for 1/3 of the day then the average speed of the message is 2.4 miles per hour. That doesn't strike me as surprisingly fast. Most of the journey would be by horseback at a trot of 4-10 miles per hour, and the average would be bought down by the ship across the channel and the various transfers en route at staging posts and inns.