At last Wednesday's full council meeting Cllr Dale Birch asked for members to support him, local CCGs and other health partners, in lobbying the Royal Borough to withdraw its application for the High Court to review the Shaping the Future consultation.
The consultation resulted in the decision to move services from Heatherwood Hospital in Ascot. Cllr Birch said a judicial review posed a "huge risk" to health provision in east Berkshire.
He added: "We need to get these changes in place right away. Delaying now will not achieve the best for our residents."
He claimed it would threaten the planned merger with Frimley Park Hospital Trust and added: "This action could put in jeopardy the plans to rescue the Heatherwood and Wexham Park Hospitals NHS Trust."
Heatherwood and Wexham Park chief executive Philippa Slinger has said that without the Frimley Park merger she has said the trust will go bust.
The majority of Bracknell Forest councillors voted to support Cllr Birch's motion in encouraging the Royal Borough to drop the judicial review.