"It is a late work of Joseph Crouch. 

Crouch & Butler were fine turn-of-the-century architects in Birmingham and produced Methodist churches, houses and books.  Churches, Mission Halls and Schools for Nonconformists ( 1901, published by Buckler & Webb, Birmingham) is their best known book, though Crouch's The Planning and Designing of a Methodist Church (1930, Silk & Terry, Birmingham) contains a plan of Beckminster.  Crouch also produced Puritanism and Art: an Inquiry into a Popular Fallacy (1910, Cassell, London).  Crouch & Butler wrote "The Apartments of the House: their Arrangement, Furnishing and Decoration" in 1900.

My guess is that Crouch was the church man in the practice and that Butler had gone by the time of Beckminster. 

The plan in Crouch's book shows a manse on the opposite side of the site to the church but it seems that this was never built."