Award-winning composer Jonathan Goldstein, his wife Hannah Goldstein and seven-month-old Saskia were believed to be on their way to Italy when the plane they were travelling in crashed at the weekend.
A family spokesman said: "We are all devastated by the news of Jonathan, Hannah and Saskia's deaths.
"We loved them all so very much. They were so happy together and we will miss them terribly.
"We would ask the media to respect the family's privacy at this extremely difficult time."
Police said a Piper plane set off on Sunday morning from an airfield in western Switzerland and was headed for Italy, but less than 90 minutes later it crashed above the Simplon Pass area near the Italian border and burst into flames, the Associated Press reported.
The bodies of the pilot, a passenger and a small child were recovered from the wreckage, the news agency said.
Mr Goldstein was the founder and creative director of Goldstein Music Group, a music production agency in London whose clients include HBO and the Royal Shakespeare Company.
Mrs Goldstein was a saxophonist who performed at venues including the Royal Albert Hall and Royal Festival Hall, and was a regular at the BBC Proms.
A Foreign and Commonwealth Office spokesman said: "Our staff are assisting the relatives of a British family who died in a plane accident in western Switzerland and are also in contact with the local authorities."