Church member mislays clubs belonging to ancient invaders? (7)

I believe the answer is:

anglian

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'church' is the definition.
(the Anglian church is the Church of England)

I can't explain the remainder of the clue.

(Other definitions for anglian that I've seen before include "English dialect" , "of German descent" , "Relating to the Angles" , "Of the tribe from which?England gets its name" .)

I've seen this clue in The Times.

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