Three people who fell to their deaths from a Glasgow tower block on Sunday are believed to have been Russian nationals who had been trying to claim asylum in the UK from Canada.

A source close to the case said the three were a father, aged 43 and named Serykh, believed to be a former member of the Russian security services, a mother, and a son in his early 20s. The source said it was a highly unusual case.

The family are said to have been trying to claim asylum in the UK from Canada, which had reportedly given them leave to stay but had denied them citizenship. They are said to have first arrived in the UK in November 2007 and came to Glasgow in autumn last year.

The bodies were found at the foot of the 30-storey block in the Springburn area of north-east Glasgow on Sunday morning.

Strathclyde police have said they will not release the identities or nationalities of the deceased until next of kin have been traced and informed. The Home Office, meanwhile, has denied that there was any UK Borders Agency activity at the property on Sunday morning after claims by some living in the area that there may have been a raid on the flat prior to the incident.

The source said the family had been in Canada from November 2000 to November 2007 before travelling through Germany, the Netherlands and Ireland to the UK, where they initially lived in Brent in north London. The source said the family had made a series of wild claims about the Canadian government.

No one at the Canadian high commission was available for comment. Their case to stay in the UK had been rejected but the Home Office was not pursuing them immediately. Their financial support had been withdrawn and they had been asked to vacate their flat. They had also been told to approach the Scottish Refugee Council and other charities for emergency assistance.

Neighbours said the three had only moved into the flat in the Red Road complex two months ago. Carol Craig, 51, and Graham Galbraith, 38, who live in the flat next door, said they were woken by police on Sunday morning who told them that their immediate neighbours had fallen to their deaths. When the couple looked over their own balcony on the 15th floor of 63 Petershill Drive, they saw three bodies on the small patch of grass below.

"We last saw them on Saturday," said Craig. "They were out on the landing. I thought it was a family. It's been such a shock. I can't get it out of my head."

The Red Road towers, at one time the highest in Europe, have been a feature of Glasgow's skyline since the 1960s, but have fallen into disrepair and are due for demolition. In recent years, they have been used to house many refugees and asylum seekers from a variety of countries, including Kosovo, parts of Africa, Iraq and Afghanistan. Paint is peeling from the walls and the small balconies are protected only by plastic mesh. The block at Petershill Drive is currently leased to the YMCA. A spokesman for the organisation said they could not comment on the nationality of those who had died.

Today small groups of asylum seekers gathered at the spot where the three died. A single candle had been lit and pieces of paper laid out on the scarred and pitted patch of grass with the words: "Freedom, please believe us."

Seyed Ali Ghasemi, 28, from Iran, who lives in an adjoining tower, said he could understand the desperation that might drive someone to take their own life. Those seeking asylum only have each other for support, he says, and everyone is worried about their own situation.

He had looked out of his window on Sunday morning and had assumed that the figures he saw at the base of the opposite tower were sleeping rough, as he himself has done in the past.

"It is very, very sad. They are scared. They are just so fed up of everything. Maybe I'm in a bad situation and I do the same thing. I have not seen my son for two years. We are all scared and fed up," he said.

Ledia Tewelde, 22, from Eritrea, said that last year she had jumped from the window of her second floor flat in another part of Glasgow, after hearing loud noises at the door and fearing she was about to be deported. She said she broke both her ankles and injured her back.

"I was very, very scared. I thought there was somebody coming into the room and I just jumped. I didn't want to go back to my country. I have been four years in this country with nothing. They give me vouchers for my food. You come from a bad situation and you come here and you are scared. It is very stressful."

Robina Qureshi, director of Positive Action in Housing, a charity that works with refugees and asylum seekers, said it was time for an overhaul of the asylum process. "This case raises serious questions about the way the UK asylum system operates in this country. Members of the public have a right to know if we have a fair asylum system or one which terrorises vulnerable people to the point they would kill themselves.

"We believe the current asylum system is based on the false premise that all asylum seekers are bogus."