The petition, which was handed into Downing Street today, was launched earlier this month by the families of two 17-year-olds who committed suicide after being arrested.
Nick and Jane Lawton’s son Joe took his own life two days after being arrested for failing a breath test.
Adrian and Ann Thornber's son Edward killed himself after being wrongly sent a letter to attend court instead of a warning after being caught with 50p worth of cannabis.
In both cases, the parents had not been informed of the arrest.
The petition calls for an end to a legal anomaly that means 17-year-olds are treated as adults rather than children when in police custody, meaning that their parents do not have to be informed of their arrest.
Police are legally obliged to contact a parent or an “appropriate adult” to offer support and advice for young people in custody aged 16 or under.
But for 17-year-olds, the decision as to whether to contact an adult is down to the discretion of the officer, unless the young person is deemed to be “vulnerable”.
Adrian Thornber said: “If we had been told about Edward, we would have been able to help him and he would still be with us today. This cannot happen to any more families. The law has to be changed."
The previous Labour government had committed to changing the law, but the plans were ditched by the coalition government.
Campaigners are currently awaiting the outcome of a judicial review on the issue, following a two-day hearing in February.
Lawyers for charity Just for Kids Law argue that current legislation treating 17-year-olds as adults in police custody contradicts both international and domestic law.
Shauneen Lambe, executive director of Just for Kids, said: “The Home Secretary can easily make this change. She has said the decision is finely balanced.
“I would hope that calls from 50,000 people across the UK and the heart-breaking stories of these two families is enough to tip the balance."
Chris Bath, chief executive of the National Appropriate Adult Network, said: “Appropriate adults are a critical safeguard for our children. The financial costs of doing so are far outweighed by the need to protect them and their families from such devastating harm.”