Three men who claim to be British have appeared in a recruitment video for the terrorist group Islamic State in Iraq and the Levant (Isis), in which they directly appeal for other westerners to join them fighting jihad and state their intention to join the war in Iraq, where the army is struggling to repel the Sunni insurgents.

The video – entitled There's No Life Without Jihad – features three men with distinctly English accents, along with two Australians, holding guns and surrounded by greenery as they implore others to join them. Captions state their nationality and noms de guerre.

A man identified as Abu Bara' al-Hindi says: "Are you willing to sacrifice the fat job you have got, the big car you have got, the family you have? Are you willing to sacrifice this for the sake of Allah?

"To all my brothers living in the west, I know how you feel [from] when I used to live there. In the heart you feel depressed. The cure for the depression is jihad … all my brothers, come to jihad and feel the honour we are feeling, feel the happiness we are feeling."

Going to Iraq or Syria to fight could constitute a crime under UK terrorism legislation.

The 13-minute video, which was apparently filmed in Syria, features clips of the seated men speaking in English, littered with Arabic phrases and words – including some quotations from the Qur'an – interspersed with footage of Isis fighters on the march.

Isis has been using its control of territory and oilfields in north-eastern Syria, where a number of jihadist groups have joined the civil war that has been raging for more than three years, to capture land in Iraq, and they are now believed to be crossing the border between the two countries with ease.

Another man, identified as Abu Muthana al-Yemeni, says the men are getting ready to fight in Iraq, where the beleaguered government has been petitioning the US to carry out air strikes to quell the insurgency. "We have participated in battles in Sham [the Arabic name for the Levant or Greater Syria] and we will go to Iraq in a few days and fight there and come back and we will even go to Jordan and Lebanon with no problems," he boasts.

He was identified in various reports as a 20-year-old medical student from Cardiff. His father, Ahmed Muthana, told ITV News that watching footage of his son had made him cry. "I wish I could hold him, hold his hand, ask him to come back," he said. "As a father, I give a message, not only to Nasser, to all the people that go from Britain to Syria to fight: please stop. Come back home."

He told the Daily Telegraph that his son had been accepted at four universities to study medicine but did not go, and that he had not heard from him since November.

In February, the younger brother also disappeared after it is thought he applied for a second passport. "To be honest, I don't agree with him, but I don't know what he has been taught in his mind," he said. "Of course I fear he will be injured or die fighting but I can do nothing. They are conservative Muslim, they don't have girlfriends, they don't talk to girls."

The Press Association reported that police visited the family two weeks ago and that is when they found out that the brothers had left.

A spokesman for the family said: "They are not happy with Nasser going. We didn't know he was going. We wouldn't let him go if we knew. My family were more devastated that Aseel went. It is heartbreaking because we don't know if we will see them again. Currently, we don't know where they are and we don't have contact with them."

"Nasser and Aseel went because they feel guilty about Syria but we were surprised they were talking about those things we saw on YouTube. Both were pious and religious and interested in the faith."

About 400 British nationals are thought to be fighting in Syria, with a majority likely to be involved with Isis or its affiliated factions, according to Charles Lister, a Middle East analyst at the Brookings Doha Centre. "This latest focus on British and Australian fighters symbolises Isis's continued determination to recruit further western, and especially English-speaking, fighters to their cause," he said.

The third Briton– and final speaker – in the video, identified as Abu Dujana al-Hindi, describes his monologue as a "message to the brothers who stayed behind".

He says: "You can be here in these golden times, fighting, or you can be on the sidelines fighting. It's your choice."

After he finishes speaking, the video concludes with slow-motion shots of the men smiling, with one apparently picking something out of his fellow fighter's beard.

David Cameron has vowed to address the threat posed to Britain by the return of foreign fighters, warning that the Sunni insurgents in Iraq were "also planning to attack us here at home in the United Kingdom".

Britain has said it will provide humanitarian assistance and counter-terrorism expertise in Iraq but will not carry out military action.