Clarissa moved quickly after receiving the carrier pigeon from her niece, Victoria. Not only did she contact the Viscount who owned the inn where Spigas was staying, but she also informed the royal family of the situation.
Victoria did not consider that for a matter as small as this, the royal family's help was needed, but Clarissa was different. She understood Andrew's importance to the country and so she notified them of anything that happened that involved him.
Victoria and the others do not realize how important their husband is to the royal family. In fact, they had proposed sending some guards with Andrew on his trip, but he had rejected them.
The reason Andrew rejected this proposal was not because he did not trust Daphne or Diana, but because he had many secrets, and having outsiders traveling with him could potentially lead to them discovering some of his secrets.