Most of the Yazidis trapped on Mount Sinjar are reported to have escaped but the Iraqi crisis continues to worsen, the chair of British-run charity AMAR has warned.

Baroness Nicholson, who founded the AMAR International Charitable Foundation in 1991, said: "As we all know, the most terrible atrocities are now being carried out in Iraq. It is a desperate situation for hundreds of thousands of men, women and children. People just like us, with lives and futures."

AMAR has 1,700 local staff and volunteers in Iraq, who provide medical and emergency aid. Regional Director Dr Ali Muthanna says the cases his team are dealing with are "heartbreaking".

"Our own staff have been in tears listening to their harrowing tales," he said.

One such story is that of three sisters who were wounded and whose mother and a fourth sister were killed during an attack on their hometown, Tel-Efer, by IS militants.

The girls themselves sustained severe injuries in the violence. Zainab, 15, had to have both her legs amputated above the knees, while 12-year-old Umama suffered a fractured femur and needed a skin graft. The third sister, Israa, required open abdominal surgery.

Despite the news that the thousands of Yazidis trapped on Mount Sinjar have managed to escape, the situation is showing no signs of slowing down.

"They are down from the mountain, but are now left to wander the roads," Lady Nicoholson told Christian Today.

"The total number [of Iraqi refugees] in Kurdistan is over half a million, and the other three quarters of refugees are in other places – wherever they can find space. Often that's in schools, which means the school term won't be able to start until next year at least. The whole country is in a very difficult situation, with much pain and suffering."

The American and British governments have both pledged to assist in the stabilisation of Iraq. The US has engaged in four air strikes against IS militants in northern Iraq, and, along with several European countries, has made aid drops.

President Barack Obama announced in a speech on Thursday: "The situation on the mountain has greatly improved. We broke the ISIL siege of Mount Sinjar. We helped vulnerable people reach safety."

However, he acknowledged that the Iraqi people were by no means safe. "The situation remains dire for Iraqi's subject to ISIL's terror throughout the country," he said.

The British Foreign Secretary Philip Hammond said that the British government would "consider favourably" any request for arms from the Kurdish forces.

A Downing Street spokesperson also said: "It is vital that Iraqi and Kurdish forces are able to stop the advance of [ISIS] terrorists across the country... We will also continue our work to ensure that Kurdish forces have the military supplies they require.

So far international efforts have not prevented the brutal acts of the Islamic State as it attempts to form a caliphate across a stretch of Syria and Iraq.

"It's getting worse," Lady Nicolson warned, noting that those coming into hospitals in Bagdad have told AMAR staff horrific stories, and teams are treating devastating, sometimes fatal, wounds.

"ISIS have dug in – their cruelty is now known globally, but they are very difficult to dislodge... At the moment, for those dying under torture, being beheaded and crucified, nothing we're doing is enough. We must do more, and we must do it on the ground, through local people."

AMAR is urging people to give generously to its Iraq appeal. To donate, click here.