Now that Peter Lane's book THE CATENIAN ASSOCIATION 1908-1983: A MICROCOSM OF THE DEVELOPMENT OF THE CATHOLIC MIDDLE CLASS  has arrived and I've had a chance to skim it, I find that there are three references to Tolkien within:
(1) page 137: ". . . there was the call by Grand Presidents and Provincial Councils for Circles to be on their guard, when enrolling new men, to ensure that men of the right 'quality' were enrolled rather than men in 'quantity'. Certainly the Association enrolled some distinguished men in this dire period [1923-1939]: there were academics such as Bodkin of Birmingham, Tolkien of Oxford, Phillimore of Edinburgh and Dixon of North Lancs, which at a completely different level there were the Test cricketers Andy Sandham of Croydon and 'Patsy' (christened Elias) Hendren of West London, who entertained many a Circle with their cricketing stories."
(2) page 153: "So, although wartime difficulties led to some Circles . . . being deprived of their Charters [through lack of unevacuated members], those very difficulties in the shape of evacuation led to expansion elsewhere. And another Circle which owed its origin, in part, to evacuation was Oxford, where many Colleges were taken over by various government departments. The opening of the Oxford Circle in October 1944 was notable, at least with hindsight, for the initiation of Frank Pakenham (later Lord Longford) and Professor J.R.R. Tolkien, the Founder Vice-President. In the light of the current interest in Tolkien's work, one would have wished for a recording of the speeches at the second annual dinner of the Oxford Circle, February 1945, when Tolkien proposed the toast to Provincial Council 'in a most amusing way which included an actual toast in Anglo-Saxon'. He was a member of the Association until 1956."
(3) page 160: "In October 1950, the Brothers of the Oxford Circle congratulated their former President, J.R.R. Tolkien, on the publication of THE HOBBIT, but could not have known that they were witnesses to the beginnings of a cult."
--As for the Catenian Association itself, it was (and is) a fraternal order like the Lions Club, Rotary, Optimists, Kiwanis, et al., only in this case drawing its membership from middle-class Catholic businessmen. It was founded in Manchester in 1908, and members originally referred to each other as "Chums", which to me sounds rather Babbitty and which I find rather hard to picture in Tolkien's case; I'm not sure if the habit persisted into the days of his membership. They were particularly interested in getting Catholic schools started, since there were far too few of these to meet the demand early in the century.
The book does cast light on just how few Catholics there were in England at the time -- while the group reached Leeds as early as 1910 and Birmingham in 1912, before World War II there were too few Catholics in Oxford to organize or sustain a local chapter. I wonder if Tolkien might have been exposed to it during his years at Leeds (a period about which we know relatively little), but if so there's no mention of it here. According to Lane's account, Tolkien must have been v. active, since he not only helped found the Oxford chapter and served as its first Vice President but apparently also as its President at some point. We also now have the dates of his membership: 1944 (when the Oxford Circle began meeting) through 1956, though no reason is given for his dropping out.
The detail about his being congratulated on THE HOBBIT in 1950 is curious, since this book was of course published back in 1937 and the second edition did not appear until 1951 (when it was released with little or no fanfare). He had finished THE LORD OF THE RINGS in 1949, but Lane's account specifies THE HOBBIT. A minor puzzle, but at least it shows that his fellow Catenians, then and now, appreciated his creative work.