Lawyers acting for the politician appeared before judge Lord Armstrong at the High Court in Edinburgh. Walker, formerly of Alloa, remained in his cell at Edinburgh's Saughton Prison where he was sent following his conviction last month.
Solicitor advocate Cameron Tait asked for Walker, 71, to be released temporarily from his 12-month sentence for the violent assaults of three of his ex-wives and step-daughter.
Walker - who refuses to accept responsibility for his crimes - plans to appeal against his 23 convictions for domestic abuse and breach of the peace at a hearing which is yet to be arranged.
He was jailed after Sheriff Kathrine Mackie heard he could not express any remorse towards victims Maureen Traquair, Anne Gruber, Diana Walker and step-daughter Anne Louise Paterson.
During the trial, Edinburgh Sheriff Court had heard how Walker - who used to represent Dunfermline in the Scottish Parliament - abused the women over a 28-year period. The court heard that Walker first struck Ms Traquair, 66, just weeks before their wedding in January 1967.
His second wife Ms Gruber, 71, described him as having a "Jekyll and Hyde" character. He repeatedly battered her throughout the late 1970s and 1980s, and Mrs Gruber alleged he raped her. Prosecutors, however, did not charge him with sexual assault.
He also struck his step-daughter Ms Louise Paterson with a sauce pan during an attack in 1978.
Before he was sent to prison, defence solicitor advocate Gordon Martin told Sheriff Mackie he was unable to deliver a full plea of mitigation on behalf of his client. He said this was because Walker could not accept his guilt and was in denial about the attacks.
Sheriff Mackie said: "Having regard to the gravity of these offences as a result of the cumulative effect of them, your extreme denial and complete absence of any remorse and the assessment of risk I have come to the conclusion that a custodial sentence is the only appropriate disposal."
Walker's lawyers then announced their client's intention to appeal against the convictions.
Had Lord Armstrong granted the request, Walker would have been permitted to stay at home pending his appeal court hearing.
But in a short, private hearing yesterday, Lord Armstrong refused to grant the request, and Walker will remain in his cell for the foreseeable future.