In a debate due to start at 8pm on Monday, peers will discuss the problems associated with the prime minister's failure to give Stowell a seat at the top table. It makes it the first time in history that there has not been a member of the House of Lords in the cabinet.
Over the past week, Cameron has come in for unexpected criticism from Conservative peers for downgrading her role. While Stowell is allowed to attend cabinet, she is not a full member and therefore will be paid around £22,000 less than the £101,038 earned by her predecessor Lord Hill.
The "regret" motion has been brought by Lady Boothroyd, the former speaker of the House of Commons, who has led protests in the Lords against the decision.
It reads: "Baroness Boothroyd to move that this House welcomes the appointment of Baroness Stowell of Beeston as Leader of the House of Lords, but regrets the decision of the Prime Minister to diminish the standing of the House by failing to make her a full member of the Cabinet; and requests that the Prime Minister reconsiders this decision."
The vote will be unwhipped and non-binding, but government ministers are expected to vote in the same way as Stowell, if she votes at all.
A spokesman for David Cameron said: "The prime minister has just carried out a ministerial reshuffle, he recognises and understands the concerns that have been raised. He wants to rectify it at the earliest opportunity, certainly immediately after the general election, if he's returned as prime minister, if no opportunity has arisen to do so over the coming nine months."
The prime minister wrote to peers last week saying the measure was a purely temporary one. He said as a general rule the Lords should be represented in the cabinet and stressed that Stowell would have the same right to speak in cabinet as her predecessor.
Initially, the Conservatives tried to get round the issue of Stowell's pay by saying the party would top it up. However, Stowell turned down this offer, amid concerns that it would not be appropriate to have a minister's salary part-funded by private donations from individuals and businesses.
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