The care minister Norman Lamb has said he will back moves to legalise assisted dying in the UK.

The Liberal Democrat made his commitment after it emerged the government would give MPs a free vote on a bill that would allow doctors to prescribe lethal drugs to terminally ill patients should they chose to die.

The proposed legislation, drawn up by the former Labour lord chancellor Lord Falconer, will be put before parliament in the coming months.

A Ministry of Justice spokeswoman said: "The government believes that any change to the law in this emotive and contentious area is an issue of individual conscience and a matter for parliament to decide rather than government policy."

Several previous attempts to change the law in England and Wales have failed and both David Cameron and Nick Clegg have said they personally oppose such a change.

However, Lamb said there appeared to be "quite widespread public support" for ending what was a "cruel" system that left relatives unsure if they would be prosecuted.

Following the case of Debbie Purdy, who succeeded in arguing she had the right to know whether her husband would be prosecuted for accompanying her to the Swiss clinic Dignitas where she would end her life, the director of public prosecutions issued new guidelines in 2010. These indicated that anyone acting with compassion on the will of a dying person was unlikely to face criminal charges. Since then around 90 such deaths have occurred without anyone being prosecuted.

Lamb said onSunday that his own conversations with terminally ill patients had swung his opinion in favour of legalisation that included sufficient safeguards.

"What an invidious situation to leave people in," he told Sky News. "Can we really be comfortable with a situation where people, acting out of compassion for a loved one who is dying, are left uncertain as to whether they will face prosecution?

"There need to be proper safeguards – that's critically important," he added. "You have absolutely got to guard against relatives or others seeking to get control of the estate. We have to be certain that it is an individual decision. I think you can meet those safeguards."

But critics – including doctors, disability campaigners and churches – warn that a formal change in the law would leave people vulnerable to pressure from family and others to end their lives.

Richard Hawkes, chief executive of the disability charity Scope, said the present legal ban was a "crucial protection" and should not be dropped. "The ban on assisted suicide sends a really powerful message countering the view that if you're disabled it's not worth being alive, and that you're a burden," he said.

He said the debate "tells us a lot about attitudes to disability. Why is it when someone who is not disabled wants to commit suicide we try to talk them out of it, but when a disabled person wants to commit suicide we focus on how we can make that possible?"

The issue has split the House of Lords in recent debates, with Lady Campbell of Surbiton, who has spinal muscular atrophy, among those warning of the dangers. But the former Commons speaker Lady Boothroyd said it was vital to change a system that added "cruelly to the suffering of people who want to die with dignity".

Under Lord Falconer's proposals, two doctors would have to sign off the fatal dose. Lamb said it remained "very hard to judge" whether it would be supported in the Commons.

The foreign secretary, William Hague, warned about the dangers of creating a "grey area" but indicated he remained open to be persuaded to reverse his previous opposition.

"I am always very concerned … that we don't create some new grey area in the law that can be misused," he told Sky. "In past years I have voted against these proposals but we'll see, I will look at it afresh, I will read the letters that come from my constituents and decide how to vote."