I was recently able to pull up an image of Anne's original baptism entry and compare to details in RA1:267. In RA1:267, her baptism is published as occurring in the town of Salisbury, church not specified, on 23 Sept. 1602.
The specific parish can now be identified as St Edmund's
Full entry: Christninges this yeare 1602 December 30 Anna :d: to fardynando Baynton gen't
Source: St Edmund's, Salisbury, Wiltshire, parish register, online image, https://www.ancestry.com/imageviewer/collections/61187/images/45582_3082375_0003-00073