Perhaps because of negative perceptions of asylum-seekers and refugees, the work of the DCRSC has remained relatively unsung in the city where it is based.
In fact, say DCRSC volunteers, negative stereotyping of these groups has been so prevalent that they have devised a slide show presentation to tackle some of the misconceptions – myth-busting, as they call it.
They point out that everyone has a right to claim asylum in another country under the United Nations Charter of 1951.
They must report to the authorities and declare themselves as asylum-seekers – and in the UK they will usually be directed to one of the holding centres, at Croydon or Liverpool.
Under the dispersal system introduced 10 years ago, local authorities have to accept a quota of refugees, and Plymouth is the main centre for Devon and Cornwall.
Asylum-seekers can apply for social housing, but one of the myths the DCRSC is keen to shoot down is that they can jump the queue.
Most refugees are offered dilapidated, run- down housing.
Mrs. Reid, who helps deliver the myth-busting talks, said: "People often want to get into a debate with us, but we refuse to be drawn into politics.
"We just say that refugees and asylum-seekers are people and deserve to live and be treated decently. We try and explain that they're not all bad people."
Asylum-seekers are not allowed to work. They get government support for housing and living expenses, but at a benefit level lower than that which British citizens can claim.
One of the reasons that the DCRSC says its services are needed is that this support is sometimes withdrawn at short notice, often through administrative error.
The charity has two paid caseworkers to help asylum-seekers through the legal process, and about 50 volunteers who give up their time to staff the centre.
Basic items of food are issued to some clients on the advice of the caseworkers, and the clothes store helps kit out recent arrivals for the unfamiliar British winter.
The centre also has an internet suite to help clients keep in touch with their families and carry out research into their cases.
To successfully claim asylum, applicants have to prove that they face persecution if they were to return home.
Hard evidence can be difficult to come by, but those who succeed in their claim will be granted leave to stay in the UK, initially for five years.
They will then be classed as a refugee and allowed to look for work.
The centre also runs women's and men's development groups, where clients are offered help to learn English and to become integrated into British culture.
Mrs Reid said the DCRSC had now helped thousands of asylum-seekers and refugees who had passed through Plymouth.
She became involved with the centre after meeting a refugee and becoming friends with him. "He's a lovely guy and he calls me Plymouth Mum," she said.
"He was one of the fortunate ones who was processed quickly, but he speaks good English and has a degree."
Mrs Reid became a supporter of the group and later answered a call for volunteers issued in its newsletter.
She said: "I enjoy it. You meet some lovely people. You don't ask questions; you just give them a smile."

Labour is to call for a revision of the international convention on refugees, arguing that it predates mass migration and leads to abuse of the asylum system.
Phil Woolas, the immigration minister, said he wanted to start a debate about the 58-year-old convention which enshrines individuals' rights to asylum from state persecution. His proposals mirror those of the French president, Nicholas Sarkozy.
Woolas said: "The Geneva convention was intended to protect individual people from persecution. A significant number of people who claim asylum are doing so for broadly economic reasons. So I think it is right we look at the framework, as indeed other European countries are doing."
He is reviving a debate launched by Jack Straw as home secretary in 2000. Straw proposed people should apply for asylum from within the countries they were fleeing or from neighbouring states. Critics said it was unrealistic to think those suffering persecution could apply for asylum from the country they were fleeing.
Woolas said there was also "a timetable issue - the recognition that some people claim asylum after several years attempting to gain migration legally". Woolas made his remarks on BBC's Beyond Westminster to be broadcast today. But he also told the Guardian he has been studying the Straw initiative, which led to protests from human rights campaigners and the UN refugee agency.
Since becoming immigration minister Woolas has not been afraid to take controversial positions, often using a tougher rhetoric than his predecessor, Liam Byrne. He argues it is dangerous for mainstream politicians to shy away from discussing migration and asylum.
Woolas has already promised that he will not allow the UK population to rise to 70 million through migration and has said some refugee advice groups have deliberately played the asylum system.
Under Straw's scheme an agreed list of "safe countries" would have been set up from which EU states would not generally consider asylum applications.
He proposed a quota system, sharing among EU states refugees from countries recognised as abusing human rights, to speed up genuine applications while keeping out false claimants.
Straw claimed that the "essential contradiction" at the heart of the 1951 convention was that, while setting out an individual's right to asylum, it does not oblige any particular country to admit him or her. The result was that "genuine" refugees often had to enter a country illegally before they lodged their claim to asylum.
The Geneva convention was drawn up during the cold war, with many of its western signatories saying it was a means of protecting victims of state persecution in the Soviet Union and eastern Europe. It was extended to apply to anyone forced to leave their country "as a result of a well-founded fear of being persecuted for reasons of race, religion, nationality, membership of a particular social group or political opinion".
Woolas stressed he was not proposing that the UK should not protect people from persecution but argued that the system needed to protect a nation from economic migrants. The EU has been working on a system designed to prevent so-called asylum shopping, where a failed claim in one country is followed by a bid in another. Britain fears the policy would mean asylum seekers could not be held in detention centres, something Woolas has said would only happen over his dead body.
Woolas has support among many mainstream Labour backbenchers. John Mann, the Labour MP for Bassetlaw, recently called on Woolas to back the rewriting of the convention saying: "Our failed system rewards those who enter illegally, stay illegally and work illegally, rewarding people smugglers whilst simultaneously being harsh and cruel on the tiny minority of immigrants - those who are fleeing death and persecution."