What was the "Group Movement'? (circa 1942)

It is the Oxford Group Movement.

"Lucy" is is CEM Joad's daughter, "AJ Russel" is Arthur James Russell, who in 1932 wrote "For Sinners Only" (mentioned on another Wikipedia page connected to 'The Group') which is categorised on archive.org under:

Topics: Oxford Group, Conversion

AJ Russell was indeed a member of that group, as its archivist.

How a group associated with 'sinners', 'alcoholics' and 'Christian awakening' might get into the focus of military matter, intelligence and counter espionage during the war in this manner?

The Group had thus come to resemble in some respects the ‘organisational weapon’ of Selznick’s description of the US Communist Party. Operating behind the scenes, putting personal pressure on key individuals, staffed by a small group who were disproportionately influential by virtue of their extreme level of commitment, the Group was becoming an unexpected rival using similar unconstitutional roads to influence, to the CP. Not surprisingly it was at this time that the Group first drew public criticism from Communist sources.

Results after 1939

The Group’s evangelism was in some respects more suited to the war and post-war conditions than it was to those of the pre-war years. The task of affecting the international crisis before the outbreak of war was too vast for the Group to make any convincing contribution by its evangelism. The attempts to reach the Nazi leaders, to surround Germany with ‘national awakenings’ and in the MRA campaign of 1938-39 to rally the leadership of Britain and America behind general statements on the Christian basis necessary for peace were inevitably ineffectual – they were dealing with far larger political forces than an evangelical group could influence. During and after the war however the major issues of national affairs in some cases were focussed on relatively small-scale local situations which the Group could affect. In particular the war effort and post-war reconstruction depended considerably on increasing production in, respectively, the armaments and mining industries. The Group quickly turned from its Battle for Peace campaign of 1938-39 to supporting the war effort. Jaeger and his team in America developed their industrial work to bring reconciliation in certain key armaments industries, before as well as after the United States entered the war. The first results by 1943 were enough to convince Senator Harry Truman, then Chairman of the Senate War Investigating Committee which had studied the home front situation, that:

There is not a single industrial bottleneck I can think of which could not be broken in a matter of weeks if this crowd were given the green light to go full steam ahead.

[…]

In Britain the Group’s tactics at the start of the war were intended, like the 1930s campaigns, to have a general influence. The 1938 MRA campaign had involved securing the support of national figures such as former Prime Minister Stanley Baldwin for general statements of Christian philosophy, and the signatures of 75,000 people for a message of support to the MRA campaign in America: it was as if the Group was trying to focus the Christian commitment of the country as a whole on the need to ‘listen to God’ in a time of crisis. This sort of approach worked more effectively in the war, when there were simple, concrete tasks that every individual could do to help neighbourhood, and thereby national, morale. The Group produced a list of such contributions that individuals could make – including ‘listening to God’ – and presented it as an expression of the nation’s Christian philosophy appropriate to the country’s need. The Group’s national network of local groups, and of contacts with civic leaders, which had been started during 1936-37, were used to distribute the ‘morale leaflet’. Some 250 ‘civic and other authorities’ co-operated in the campaign. Systematic coverage was made of particular areas – such as the Battersea campaign of January to June 1940. Led by two vicars in the Group, sponsored by the Mayor and MP and staffed by the Group’s full- and part-time London ‘teams’, the campaign included the visiting of 10,000 homes, many of them several times, and a Town Hall meeting for 1,000. By February 1941 people trained on this campaign had started similar undertakings in thirteen areas in or near London.580 Local groups outside London helped evacuation measures run smoothly, and one of the Group’s full-time workers produced a film of a successful evacuation run on Group principles.

— David C. Belden: "The Origins and Development of the Oxford Group (Moral Re-Armament)", Dissertation, Oxford, 1976. (2018 online edition PDF)