Conrad Quashie, Bruno Melling-Firth and Maximilian Boomgaarden-Cook, all 19, were travelling from the capital Bangkok to the northern city of Chiang Mai.
The three friends had arrived in Thailand only last week for their gap year.
Their coach was involved in a collision with another bus in Khlong Khlung, in Kamphaeng Phet Province.
Mr Boomgaarden-Cook’s father said the family had been left in “unbearable” pain after the crash.
All three had studied together at the Charter School in Dulwich, south London.
At least two other foreigners were also on the bus, one of whom required hospital treatment.