The centre on Cross Street offers English lessons and dance classes, as well as providing food, clothes and other support services.
However, cuts mean the Centre has now been forced to close for all but one day a week.
Ms Stevenson, who is known for her roles in films like Bend It Like Beckham and Mona Lisa Smile, is backing a new campaign that aims to raise £30,000 in time for Christmas – a sum which would allow the charity to open for two days a week from January.
Jo Cobley, Head of Development at the charity, said that she was “delighted” with the £15,000 already raised by the appeal so far, but was conscious that “we’ll only reach the target if people keep on giving as generously as they have been”.
Cobley added that the charity was helping to foster “a sense of pride and ownership” in the community around its work with refugees and migrants, and that this would be key to creating a more sustainable fundraising platform in the future.
The campaign has focused on raising money through online donations, spurred on by an fundraising video featuring Stevenson.
Featured image: Flickr-Creative Commons