There doesn't seem to be an official website for St Mildred's at the moment. They have had stmildreds.com registered but nothing seems to have come of it.
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St Mildred's lies on the corner of Bingham Road and Sefton Road. St Mildred's Centre (the church hall) is on the west side of the church with the vicarage now relocated to Sefton Road on the south side.
An aerial view of the church is available on Windows Live Search Maps.
The parish basically covers the parts of Addiscombe bordered by the old railway line from Woodside to Selsdon (now part of Tramlink) to the west and north, Shirley Road to the east and Addiscombe Road to the south. However 20th Century residential development east of Shirley Road and south of Addiscombe Road adds two largely self contained areas to the parish. Ashburton Park lies outside the parish.
The parish was originally part of St Mary Magdalene. In 1912, following the building of a number of houses on the former Ashburton estates, a building named Gordon Hall was rented as a place or worship and in 1914 a proper chapel-of-ease was opened (later known as Addiscombe Hall). In 1921 St Mildred's Hall (later known as the Small Hall) was opened and in 1922 the area was separated from St Mary Magdalene and became a Peel District.
The church was built between 1931 and 1937 to the designs of C G Hare. In 1932 it was consecrated and St Mildred's became a parish. At that time the church just consisted of the nave. The chancel, with the low tower which provides light to the altar, followed in 1934. The New Hall was opened in 1935. The Lady Chapel on the east side was added in 1937.
The church is built of brick in a round arched style and is felt to have something of a 'cinema' look about some of the detailing.
Clearly the entrance, which is quite elegant in its own way even if it perhaps doesn't quite blend in with the main building, and St Mildred's Centre are much later additions to the building. My understanding is that they are indeed brand new additions built by Pegasus Retirement Homes along with a new vicarage in return for the church surrendering the site of the old vicarage for development.