Reading Sarc Campaign spokeswoman Kirsty Lowe said the stance taken by Thames Valley chief constable Sara Thornton and NHS Berkshire - reported in last week's Chronicle - came as "such a shock".
Kirsty, who estimates the cost of running a centre, which has to be funded by police and health authorities, would be up to £3m a year, added: "We are even hungrier now. We will not be quiet and are not going away."
She said a centre could be purpose-built, or accommodated within existing hospital or charity buildings. A Sarc houses multiple services under one roof for victims of sexual assaults, including forensic and counselling, and are often the first port of call for those wanting to report an attack but are worried about going to the police.
One Reading woman told the Chronicle she waited four days to go to the nearest Sarc in Slough because she was physically unable to drive, did not want to take public transport and could not afford the return taxi fare.
The woman, who believes she was the victim of a drug rape, was eventually driven to Slough by a friend and said more needs to be done to inform people about the Sarc, and added: "My big problem was by the time I got to Slough, I was too late for blood test forensics. If there was a Sarc in Reading, I could have done something much sooner."
Kirsty said the campaigners will continue to lobby police and health authorities to reconsider. She added: "We are not even aware of any conversations between the two parties."
Campaigners have launched an on-line petition calling for a Sarc in every town with a population over 120,000. If the petition is signed by 100,000, it will trigger a debate in the House of Commons.