Willetts Bakery and Tearooms has been operating from premises in Thames St since the business was bought by Matilda Willetts in 1920.
There were another three owners before the business was bought by Mrs Smith and her husband, Garry, in 1987.
Today is the last day of business at Willetts, with the Smiths relocating five doors along the street and opening a new cafe, Bean on Thames, next week.
The same products will be on offer, including long-time favourites mutton pies and custard squares, and the service will be the same, but the Willetts name will be no more.
Mrs Smith said the Willetts name belonged to the current premises and it did not seem right to shift it.
The new premises were modern and more user-friendly, she said.