The MP, who chairs the All-Party Parliamentary Group for the Armed Forces Covenant, has received scores of complaints from military families who find they struggle to get their children into local schools when they receive new postings often at short notice.
Highlighting the difficulties faced to her colleagues, Mrs Trevelyan said: "The present school admissions system is structured towards two admissions per academic year, meaning that any child seeking admission outwith that framework must simply hope that the school they prefer has capacity.
"That is all well and good, but military families do not have the luxury of timing their moves within school admission timetables. By not taking into account military families' unique and challenging situations, councils are failing to live up to the commitment they pledged to uphold when they signed the community covenant."
The Bill calls for military children to have high priority in the school admissions system, to help offset the educational disadvantages they face as a result of their families’ service to the nation.
Explaining what she hoped to achieve with her Bill, Mrs Trevelyan said: "Our education system is already geared to acknowledge that some children face exceptional and difficult circumstances and that they will need priority when it comes to admissions to help offset the difficulties that they have already faced. That is why looked-after children have top priority when it comes to admissions.
"The Bill seeks to recognise that military children face significant upheaval and educational disadvantages through no fault of their own and that they too should have high priority for admissions in light of that.
"The Bill would have the secondary effect of easing the pressure on military families, who are often faced with short-notice moves and must then work out how to transport their children to schools miles from base because they face disadvantage in the schools admissions system."