As the aid-worker's body has not been found, her picture was placed near the altar in Westminster Cathedral in the absence of a coffin.
Cardinal Cormac Murphy-O'Connor, archbishop of Westminster, said on Saturday in his sermon Hassan had become a symbol of goodness and called her a "peacemaker in a time of seemingly endless wars".
In a tribute read out at the service, which was also open to the public, Hassan's three sisters and brother said: "To the rest of the world Margaret was an extraordinary charity worker. She had tremendous compassion for her fellow man and had unfailing belief in the capacity of the human heart.
"Our loss is not for the charity worker; our loss is for the woman who was our sister."
Hassan was kidnapped on 19 October as she was being driven to work in Baghdad, where she was director of the local operation of aid organisation Care International.
A video tape released to Aljazeera last month showed a hooded figure shooting a blindfolded woman in the head.
Hassan was kidnapped on 19
October on her way to work
Hassan's Iraqi husband and British Foreign and Commonwealth Office officials have said they believe the tape is probably genuine and her family say they believe she is dead.
US marines found the mutilated body of a Western woman in Falluja last month during an assault on armed fighters in the city, but the foreign office said dental records proved the remains were not those of Hassan.
Irish-born Hassan, 59, moved to Iraq more than 30 years ago after marrying an Iraqi engineer. An obituary in the service sheet detailed her long career as an aid worker and language teacher and quoted a tribute to her which had been posted on a website: "The world needs more people like this lady."