Children of the Heavenly King hymn tune
Hymns are written to standard metres (for example the metre for Children of the Heavenly King is 7.7.7.7) so it is possible to set any hymn to any tune of the relevant metre. British and American Christians sing essentially the same hymns and use the same tunes, but the hymns and tunes are often paired quite differently. People who lived in England during the war would have been most likely to sing 'Children of the Heavenly King' to the tune 'Innocents', which is the most common tune in British hymn books of that period. It is certainly the tune that I am familiar with from my childhood in the 1950s.
Mrs Miniver has the hymn set to 'Pleyel's Hymn', a fine tune, but one that would rarely or never have been sung by a British congregation.