A spokesperson for HMP Bronzefield said it could not provide information about specific individuals but said all prisoners had full access to healthcare, including attendance to “external medical facilities if needed”.
They said: “Any prisoner refusing food receives regular medical assessment and support from clinicians, as well as being offered mental health support.”
The prison said all prisoners were managed in line with policies to assess “individual risks and security status”.
Posting at 13:00 GMT on Wednesday, Sultana said she would not leave the prison until an ambulance arrived to transfer Ms Zuhrah to hospital.
Protests are currently taking place in five different prisons involving eight people, including Ms Zuhrah, who have all been charged with and denied offences relating to alleged break-ins or criminal damage on behalf of Palestine Action, before the group was banned under terrorism legislation.
A letter by lawyers representing the group, seen by the BBC, told Lammy there was a “real and increasingly likely potential” their clients would die in prison as part of their protest.
The BBC has contacted Sultana and the Ministry of Justice for comment.
