Scottish Liberal Democrat leader Willie Rennie, the former MP for Dunfermline, is set to ask for legal advice on ways of stopping Walker from collecting his resettlement grant of £29,048 if he clings on to his Dunfermline seat until the next election in 2016.
Current Labour Dunfermline MP Thomas Docherty is also set to bring a bill to Westminster lowering the minimum prison sentence from a year and a day to six months at which an MP, MSP or Assembly member in Wales or Northern Ireland will be automatically disqualified from office.
The moves come as concerns were raised that Walker, 71, cannot be disqualified because he received a summary trial in a sheriff court, meaning that he can only be handed a maximum sentence of 12 months.
Walker was ejected from the SNP last year after details of how he beat three former wives – Maureen Traquair, Anne Gruber and Diana Walker – and stepdaughter Anne Louise Paterson emerged.
Questions have been asked about why the SNP did not check his background properly and whether party chiefs failed to heed warnings about him over crimes dating back more than 30 years.
Rob Armstrong, the brother-in-law of the MSP’s third wife Diana, said he handed documentation to Deputy First Minister Nicola Sturgeon’s parliamentary office. Her office said Ms Sturgeon was unaware of the information and has joined calls for Walker to step down.
Mr Armstrong has called for SNP chief executive Peter Murrell to consider his position.
Labour Fife MSP Claire Baker said: “Mr Armstrong deserves an apology from the SNP for their conduct in this whole situation and he is quite right in calling for action now.
“We need to know what the leadership knew, when and who made the decision to allow Walker to become a candidate despite these serious allegations. I agree with Mr Armstrong that Peter Murrell must consider his position in light of this.”
On changing the law, she added: “Scots deserve the highest standards of integrity from their elected representatives, and those convicted of violent crime should not be allowed to continue in their post. There needs to be a change in the law.”
A Scottish Conservative spokesman said: “It is unacceptable for people like Bill Walker to continue as a member of parliament. We will examine any proposals brought forward to prevent this from happening again.”
SNP parliamentary business manager Joe Fitzpatrick has backed a change in the law and is considering a debate on Walker’s future.
He said: “It is not currently within the parliament’s competence to establish measures for removing MSPs from office.
“Under the current arrangements in line with the Scotland Act, it is up to Mr Walker himself to stand down and, given the serious and heinous nature of his crimes, we would urge him to do so immediately.”
But with retrospective legislation unlikely, meaning any new law could not affect Walker, the Scottish Lib Dems said that the best course of action would be to stop him profiting from staying on as an MSP.
Mr Rennie said he hoped Walker would stand down. He added: “We can’t have wife beaters profiting from parliament.”
Meanwhile, campaigners against domestic violence have criticised the Crown Office’s decision to take the case to a sheriff court.
Lily Greenan, the head of Scottish Women’s Aid, said last night: “We now have a picture of a serial offender, so there is a question of what is the basis on which it was moved from being a solemn trial?”