Another piece for the jigsaw! Good to hear.
Have you considered that 'Bridget' in the 1939, may actually have been 'Beatrice' (perhaps person capturing the info misheard her name), or are you aware of Beatrice elsewhere? The record seems to have been re-numbered from original written order, to show her as '2', between Hugh and the blanked out child. Or, could Beatrice have already died (no obvious death entry though), or have just left, and Bridget be a 'second wife'?
John C(harles) Garrity , born Dec 1933, is re-numbered as '4', so immediately after Hugh, Beatrice and blanked out child . I can see a John C Garrity birth entry in the 1st quarter of 1934, with mother's maiden name 'Plunkett', but not seeing a corresponding marriage so far. There is another male child born 1932 to same parents. Both Stockport district, which nowadays is Greater Manchester area. You said John Charles Garrity died in 1964, so his death certificate might provide some answers.
I also notice 6 Births to Garrity/Eccles parents in Bolton district between 1927 and 1937. As Hugh and Beatrice married in Bolton district in 1928 and I can't see another Garrity/Eccles marriage in area for same timescale, were these their children? Where are they in 1939 (I can see two possible infant deaths for the two given same first name)?