The apartment was on the 4th floor and the noise didn't bother us at all. I don't think you should make Soho your choice if you expect a quiet night. The address is right in the thick of it, not far from the underground and has plenty to do and places to eat. Particularly try cocktails at the bar directly opposite, it's a great place with really friendly staff. There's also a great French cafe down Greek Street for breakfast. Soho/Covent Garden is the best place to access the best of London.
Don't expect a really cool state of the art apartment, it has everything you need (you might want to take a towel!) and it's clean. Oh, the tv reception is very poor, take Netflix!