Ashraf came to Britain from Bangladesh in 1968 and was already betrothed to Sufia, who was still a child in Bangladesh. Before he returned to Bangladesh to be married to Sufia, he met and had a fling with Stella, a young hippy, and their relationship continued on and off after Sufia emigrated to Britain to be with her husband in 1973. Sufia knew about Stella, and suspected other affairs and found them all distressing.
In the beginning, Ashraf worked in a car manufacturing plant in the Midlands. Later on, relatives in Walford East London offered him a job in one of their corner shops and he, Sufia and their two small children, Shireen and Sohail, came south to live. He saved enough money to open a business of his own, although racist taunts and attacks made life difficult for him. Even so, by putting in long hours he finally made a success of running his third shop in Walford High Street.
Ashraf is the second cousin of Saeed Jeffery and upon Saeed's return to Bangladesh in 1985 he takes over ownership of the flat above the Jeffery's grocery store, First Til Last. Ashraf first appears in July 1987, when he comes to inform the tenants, Sue and Ali Osman, that he is selling the flat. Ali wants to buy it but cannot afford it and so the flat is sold to Alan McIntyre. In January 1988, Ashraf employs cousins in his shop in Walford, which leaves him free to buy and run First Til Last in Bridge Street, which is owned by Saeed's wife Naima and has been run by her cousin Rezaul Gabir until the Karims' arrival. The Karims then move into a house in Victoria Road, which was previously owned by the hairdresser, Julie Cooper and Ashraf sends his two children to private school.
The first thing Ashraf does is hire Arthur Fowler to work at the First Til Last. However problems arise when Arthur manages to offend one of their Asian customers by including a meat product in her delivery. Ashraf decides to punish Arthur by giving him the humiliating task of being the paper delivery boy. After much teasing from the Walford residents Arthur dumps the papers without delivering them, causing many angry complaints from irate customers. Ashraf then decides that Arthur has to write each customer a letter of apology and personally deliver them, further humiliating him. Animosity between the pair only worsens and by July that year Arthur is sacked.
The Karims keep themselves to themselves, and Ashraf is particularly protective of his daughter, Shireen. He becomes extremely concerned when she starts spending a lot of time with Ricky Butcher and he tries to nip their blossoming relationship in the bud. However Shireen continues to see Ricky behind his back and when her brother, Sohail, reveals the relationship, Ashraf is furious. He bans her from seeing him and bans Ricky from his shop. Ashraf decides that the only way to stop her from fraternising with undesirable men is to marry her off to an eligible Muslim suitor - much to Shireen's dismay. Muslim culture dictates that betrothed women must be virgins before marrying and so in the light of her dalliance with Ricky, Ashraf decides that Shireen has to have a virginity test performed. He marches her off to Dr. Harold Legg and demands that he performs one, but is refused. Ashraf becomes incensed at Dr Legg's refusal and is even more enraged when he has the audacity to suggest that he should put aside his traditional values and embrace western ones.
In November 1989 Sufia discovers that Ashraf is still carrying on with his mistress, Stella. Sufia decides to pack her things and threatens to leave. However Ashraf manages to talk her into staying and promises that his affair is over, which is true as Stella had grown tired of being his mistress and ended their relationship. Ashraf sets about arranging a marriage for his daughter. Despite Shireen's misgivings she is actually pleasantly surprised when she meets her suitor, Jabbar Ahmed and they become genuinely attached. Meanwhile Ashraf manages to talk Stella into reigniting their affair and he regularly sneaks away to be with her. Sometime later, though, Jabbar's uncle spots Ashraf with Stella, in a restaurant, and realises the Karim family are not as honourable as they seem. The Ahmed's cancel the engagement and Shireen is left mystified and upset, while Sufia feels angry and betrayed at Ashraf's renewed adultery. Ashraf then decides that the only solution is to leave their shop in the hands of his cousins and move the family to Bristol. Before they leave, Shireen's mother and the women of Jabbar's family help the young couple to meet secretly to keep the engagement going. Whether it took place or not is never stated as the Karims leave town soon after. The Karims' last appearance is in June 1990.