Two-thirds of parents back random testing amid concern that secondaries are not doing enough to tackle youth drug culture.
Four in five worry that their child has access to drugs at school, according to a survey by polling company IFF research.
There have been several recent high-profile cases of pupils being caught with drugs at school.
Last month, Ben Wonnacott, son of TV antique expert Tim Wonnacott, was suspended from Eton after a stash of cannabis was found under his sink.
Research for a Channel 4 documentary, This Teen Life, broadcast last September, found that more than half of 14 to 19-year-olds had encountered people selling drugs or alcohol in their school.
Nearly half of parents believe testing would be the most effective way of reducing drug abuse by teenagers, compared to fewer than one in five who favoured information campaigns aimed at teenagers and one in nine who supported a greater police presence near schools with drugs problems.
Heavier penalties for teenagers caught with drugs and the appointment of a new government "tsar" attracted even less support.
Concern about drugs was greatest in Scotland where almost all parents (95 per cent) admitted to being worried about the situation.
The findings are the result of 640 face-to-face interviews with parents and guardians of teenagers in the UK carried out for drug-test supplier Euromed whose clients include NHS Trusts and the UK Prison Service. John Fritz, Euromed's managing director, said: "Random testing has proven a successful methodology for tackling drug misuse."