Swanage on Wikipedia.
 

All Saints on Redcliffe Road, as seen by Streetview in 2014. This source dates it to 1956-7. SZ 0298 8009. Link.

Ebenezer Wesleyan Chapel on Bell Street is dated 1861, and was seen by Streetview in 2019. According to this source there is some doubt as to whether it was originally Wesleyan or Primitive Methodist. An appended comment says it was closed no later than 2009. SZ 0174 7896.

Emmanuel Baptist Church (2019 Streetview) on Victoria Avenue. SZ 0176 7908. Link.

Holy Spirit and St. Edward (R.C.) on Victoria Avenue. SZ 0297 7910. © Graeme Harvey (2011). Three additional views - 1, 2, 3, all © Martin Richter (2012). Link. Grade II listed - dates it to 1904.

Kingdom Hall of Jehovah's Witnesses on Court Road and Hanbury Road, as seen by Streetview in 2019. SZ 0248 7882.

The local Quaker Meeting is shown by Google Streetview to be on on High Street. The building however appears to be Methodist owned, so do they meet here? Their website doesn't appear to provide an address.

Available O.S. maps up to the 1948 edition show St. Aldhelm's Church on Park Road, at SZ 0325 7842. The building on its site was seen by Streetview in 2019.

St. Mark (2019 Streetview) on Bell Street. Pensner dates it to 1869-70. Link. Grade II listed.

St. Mary the Virgin. SZ 0272 7878. From an old postcard in Steve Bulman's Collection. A modern view, © Graeme Harvey (2011). Link. Grade II listed, which says only the tower is medieval. A separate graveyard across the road has a grade II listing for its wall and some tombstones.

The Salvation Army Church (2019 Streetview) on High Street. SZ 0302 7875. It pre-dates a map of 1888, where it's labelled as Mission Hall. The other side of the building, seen from Kings Road East by Streetview in 2018. Link.

Swanage Methodist Church, a rather handsome building on High Street, as seen by Streetview in 2019. Older O.S. maps label it as Wesley Memorial Church, and Pevsner dates it to 1886. SZ 0286 7869. Link. Grade II listed.

U.R.C. (2017 Streetview) on High Street. Older maps label it as Congregational. Its grade II listing dates it to 1837, with later extensions. It had a predecessor of 1705. SZ 0273 7871. Link.

 1" O.S. maps of mid-20th century vintage show a place of worship roughly in the middle of a block of land defined by Cliffe Avenue, Burlington Road, Ulwell Road and Victoria Road. In all likelihood it was the predecessor of All Saints, a wooden hut, mentioned here. Its exact placement is unclear, but it will have stood somewhere along the left side of the road seen in a Streetview from 2014. SZ 0308 7996.