I will not speak to the essence of the question, but I will speak to the reasons that he saw to having Mosley released.

Mosley's second marriage was to one of the Mitford girls, specifically Diana. The Mitfords were very closely related to the Churchills, through Clementine Oglivy, who was Diana Mitford's grandmother. Lady Clementine's sister, Lady Blanche, was Winston Churchill's mother-in-law.

There were ongoing allegations that Diana Mitford's grandfather, Bertie Mitford (and Lady Clementine's husband), was actually Clementine Churchill's natural father.

The Mitford children had grown up playing with Randolph and Diana Churchill. Randolph Churchill stood as godfather for Jonathan, Diana Mitford's son by Bryan Guinness, her first husband. (Diana Mitford's divorce from the heir to the Barony of Moyne resulted in her exile from a great deal of London Society, to say the least.)

Winston Churchill had a great deal of affection for Diana as well in her youth, but I'd say his son's ties, with having practically moved in to Diana Guinness' home during her marriage to Bryan, were far stronger. Churchill did solicit her opinions on Hitler in the 1930s. He'd disassociated himself from her entirely at the time of her divorce, but his first luncheon with her after her divorce and subsequent involvement with Mosley was about asking what she'd thought during her visits to Germany to see her sister, the Hon. Unity Mitford. (Unity Mitford is the subject of great interest herself — the daughter of an English lord who fell in love with Hitler.)

Churchill also had an interest in Mosley early on — he'd proposed him for membership in his Other Club, which he'd founded in 1911.

Churchill arranged for Diana Mitford and Oswald Mosley to be interned together, at the request of Tom Mitford (Mosley's brother-in-law through Diana), Baba Metcalfe and Walter Monckton.

Regarding his eventual release, he'd been ill for years at the time of his release and Lord Dawson had argued for his release as early as June 1943, which prison officials opposed, but by November 1943, the prison agreed that Mosley should be released, although politically it was impossible. Clementine Churchill pointed out to Diana Mitford's mother, Sydney Bowles (Lady Redesdale) that if they were released, they would likely be lynched.

The Home Secretary, Lord Morrison, was opposed to the Mosley release, but Churchill supported it, and in fact had never been in favour of imprisoning the Mosleys.

I must assume that his close connection to Diana Mitford, as well as the influence of their shared family members, was extremely influential in how he felt about the Mosleys' imprisonment.

A good source on the Mitfords, and therefore, tangentially Mosley, is Mary S. Lovell's The Sisters. This integrates a great deal of research into their papers and letters, including an examination of Churchill's papers.

An Internet-viewable source that touches on some of this is in The Daily Telegraph.