The suspect was caught on CCTV entering St Nicholas Church and sitting at the back, before taking the victim's bag and leaving.
A 90-year-old woman had her money stolen during the Ash Wednesday service on February 18 at around 8pm.
The suspect has been described as a black man, around 30-years-old and 6ft tall, who was seen wearing blue jeans, white trainers and carrying a bag.
During the service, the elderly woman had gone up to the alter and left her handbag by her seat on the floor but when she returned it had gone.
Parishioners searched the local area and found the bag with the woman's personal belongings dumped in a nearby street, but cash from her purse had been taken.
Reverend Andrew Downes said: "It's a mean crime.
"The man is believed to have crept in and out in five minutes.
"The lady herself was very shocked.
"We want to get the guy caught as he will carry on doing it.
"Crimes like this in a church are unbelievable."
Anyone with information about the identity of the suspect should call police on 101, or call Crimestoppers anonymously on 0800 555 111.