Rima and Michael Lynch thought they and their children would be safe from racial abuse when they moved to a Catholic working-class area close to central Belfast.

But the mixed-race couple's experience over six years puts a human face on the rise of race-hate crimes in the city, beyond Protestant/loyalist areas with a reputation for xenophobia.

Rima, a Christian-Israeli Arab, has been branded a Roma, Romanian, "Jew whore" and "dirty Arab" by a family who have subjected her family to a slew of racist abuse and intimidation.

The Guardian has learned there have been 13 arrests linked to race-hate attacks in Greater Belfast since the start of last month. But the Lynch family say the Police Service of Northern Ireland (PSNI) in south Belfast has failed to act against local people who have terrorised them in the nationalist Lower Ormeau area.

PSNI statistics show a sharp increase in race crimes and racist incidents in the past two years. In 2012/2013 the PSNI recorded 470 racial hate crimes but that figure rose to 691 to the year ending March 2014. In the same period incidents of racial abuse and intimidation rose from 750 to 982.

When Michael Lynch, who met his wife in Israel, moved back to his native Belfast he decided it would be safer to live in the Catholic Lower Ormeau Road area than in a loyalist area. The Lynches say they and their three children were targeted by a local woman, her husband and children, who objected to the presence of immigrants in their midst.

"At first they said I was Roma and then later Romanian," Rima said. "When I finally spoke to this woman I told her I was an Arab-Israeli, born in Galilee. At first I was called a 'Jew whore' for being Israeli and later when I reminded neighbours that I was an Arab-Christian I was branded a 'dirty Arab'.

"At first it was low-level intimidation with our windows being rapped violently at night when we were watching television in the front room, or our plant pots turned over in the street, or local kids banging the door. Later they targeted my two sons on social networks, repeating the racist slurs and later the real bullying began against the boys," Rima said.

Her husband said the racist bullying of one son got so bad he had to take him out of a local Catholic secondary school. "I couldn't believe this was happening in a Catholic area where I wanted the family to settle. It was near to work, close to the city centre, not far from the university district and some good schools. But after all we have been put through we are seriously considering moving out to another part of Belfast," he said.

His wife said the children of the family behind most of the intimidation called her sons and daughter "monkeys" and told them to go back to Israel. "They bullied a single Polish mother and her children out of the same area and I know for a fact they are putting pressure on an African lady who lives in the same street. Yet the police up until very recently were not prepared to take action against these people," she said.

Rima stressed she had "many, many good friends" among the locally born population in the Lower Ormeau but believed neighbours were terrified of their tormentors. She added: "In a strange way I could cope with this better if it was happening in a loyalist, Protestant area. At least they are upfront and open about the way some of them in that community treat foreigners. In this area, among people of the same faith, it is more a case of being smiled at to your face and then stabbed in the back."

A woman looks at racist graffiti written on the walls of a house recently occupied by two Nigerian men. Photograph: Stephen Barnes/Demotix/Corbis

However, most recent attacks have undoubtedly taken place in loyalist working-class redoubts such as east Belfast and Newtonabbey on the northern outskirts of the city. Among those targeted in loyalist communities was Palestinian nurse Mohammed Samaana, who has worked in the NHS since 2000. He said even some of his patients had verbally abused him.

He said: "A female patient told me: 'You are not from here and I resent all foreigners who come to Ireland.' The worst experience of racism though was when I was attacked in the [loyalist] Sandy Row area and I felt my life was at risk."

Samaana said he was more concerned about being a Muslim in Northern Ireland after the comments of Pastor James McConnell, who called Islam "satanic". McConnell initially received the support of the first minister, Peter Robinson. Both Robinson and McConnell later apologised for their remarks, which included Robinson stating that he would not trust any Muslim that adhered to sharia law.

Samaana said: "In general I'd say Belfast was initially welcoming but it is gradually changing for the worse. It feels like the I way I was treated when I first came to Northampton, in England, where people had very negative attitude towards people like me and where I faced social exclusion and alienation, which made me leave. They say Muslims don't want to integrate. In my experience, and in the experience of others I know, many Muslims do want to integrate but we feel shunned most of the time."

Jonathan Tongue, author of The Democratic Unionist Party: From Protest to Power and a University of Liverpool lecturer, blamed "post-Troubles paranoia" for the rise in racism in Protestant areas. "These people are used to having a united identity and they are not used to outsiders in their midst. Catholics were driven from their areas decades ago so they are stunned by this recent wave of immigrants coming into their communities.

Anna Lo at an Alliance party conference. She received verbal and physical threats from racists in Belfast. Photograph: Stephen Barnes/Demotix/Corbis

"In addition, the old enemy they fought isn't around any more now that the conflict is over, although sectarianism is far from dead. So they have found, due to globalisation, a new imagined enemy in their areas."

Tongue said that while many loyalist political leaders were opposed to the attacks, they sometimes happened spontaneously. "There is a bit of a Millwall mentality within working-class loyalist communities – the perception that 'no one likes us, we don't care'. They don't see how much damage these attacks are doing to their own image, their own communities even if, to be completely fair, loyalist leaders on the ground see this. Most importantly, there has been no economic or social 'peace dividend' for the loyalist working class and now they see immigrants coming in who are competitors."

In Catholic districts there have been some anti-immigrant problems around Dungannon, in County Tyrone, but such incidents have mainly occurred in loyalist communities.

Meanwhile, Anna Lo, the UK's only Chinese-born parliamentarian, who has been subjected to verbal and physical threats from racists in Belfast, said she had been "absolutely overwhelmed" by support she received after expressing fears over the rise of racism, but reiterated that she was quitting politics.

Lo, who represents the Alliance party in the Stormont assembly, said: "The people in general are wonderful here and I was inundated with cards, messages, flowers and gifts after I told the Guardian I was fed up with local politics. The good people have convinced me at least not to leave Northern Ireland and move to England where my sons live. But as for political life, I don't see a future for me beyond the next assembly elections in 2016. It's time for a new generation to try and challenge the racists and the bigots."