Solihull Metropolitan Borough Council lists 20 conservation areas: Ashleigh Road, Barston, Berkswell, Bickenhill, Castle Bromwich, Granville Road, Grove Avenue, Hampton in Arden, Knowle, Malvern Hall and Brueton Avenue, Malvern Park Farm, Meriden Green, Meriden Hill, Olton, Solihull, Station Approach Dorridge, Temple Balsall, Walsall End, Warwick Road and White House Way.
None of the 20 carries a Shirley name. The council notes that a conservation area may also carry an Article 4 Direction removing further permitted development rights, and names none. We found no Solihull guidance on lime or breathable finishes.
We would explain how you check the conservation boundary, any Article 4 direction and the proposed work before confirming whether permission is needed. That answers it on the render page instead of on site.