Amy Ransom died after falling from a mountain
The recent deaths of Amy Ransom, 17, on a school trip to Vietnam and of Bunmi Shagaya, 11, in France, show the need for the government regulations to be reformed, the Association of Teachers and Lecturers (ATL) says.
One of the largest teachers' unions - the National Association of Schoolmasters Union of Women Teachers (NASUWT) - has urged its members not to get involved with school trips because of the dangers involved.
The rise of the "blame culture" means many face losing their jobs if a pupil in their care is injured or killed, the NASUWT says.
'Over-reaction'
But the ATL believes this to be an over-reaction and instead wants to see clearer guidelines for schools when taking pupils on educational visits.
"I know that you will share the very widespread concern at the tragic recent deaths of pupils on school trips," ATL general secretary, Peter Smith, says in his letter to Ms Morris.
"I think you will also agree that to suggest that no trips should take place in the future is nonetheless an over-reaction," he writes.
"The future of valuable school trips is at stake, the government must act now."
Current guidelines, introduced in 1998, have provided a useful framework for schools, Mr Smith says, but they must be reviewed on a nation-wide basis.
Risk assessment
Schools should be legally required to inform their local education authority about any trips and risk assessment forms - completion of which is currently optional - must be "clarified, updated and more focused".
The Adventure Activities Licensing Authority (AALA) should be expanded to cover not just commercial activity providers, but members of voluntary organisations such as the Scout movement, Mr Smith argues.
"The remit of the licence must be extended to cover activities previously ignored - so-called "dangerous sports" such as climbing on a specially built wall, hang-gliding, archery and sub-aqua activities," the letter says.
And teachers supervising water activities, which have been the cause of many recent tragedies, need more specific guidance, he concludes.