For apartments in Rome, I know some people who live in Rome speak very highly about using cross-pollinate when looking for an apartment throughout the city. It was started by an American Couple, Steve Brenner and Linda Martinez, who moved to Rome 15 years ago. They started a small, sort of hip B&B, an noticed that there was almost never a vacancy, such is the demand for apartments. So, they started cross-pollinate, where they seek out nice apartments, vet them thoroughly, and act as a booking agent for a nominal fee.
They are very trustworthy, and it takes some of the risk out of renting from a stranger on BnB, where surprises are not uncommon. There is also the benefit that if something goes wrong, there is a physical place where you can go to go to and talk them about it at their B&B, as opposed to trying to sort out a problem with someone who is renting their apartment to you while they work in London. They have places spread throughout the city, and have started vetting and listing apartments in Florence, Venice, and other cities.
http://www.cross-pollinate.com/about