This is a fascinating, unexpected gem in the woods, that even some locals do not know about.
Although not a whole church, this church wall dates from before 1541. St Mark's is the only civic church in the country and the chapel had originally served the Hospital of the Gaunts. It was surrendered at the Dissolution and purchased by the Council in 1541, becoming known as the Mayor's Chapel, although it was not called the Lord Mayor's Chapel until 1899, when the office of mayor was elevated by Queen Victoria
In 1822 the original West window was removed from the chapel at the bottom of Park Street and was purchased by Henry Brooke of Henbury Hill House who 'set it up in a sham ruin on Henbury Hill to serve as an object from his house'.
Some more information is here. http://museums.bristol.gov.uk/details.php?irn=108580
It's a Grade II* listed building. See here.
https://historicengland.org.uk/listing/the-list/list-entry/1282073
A footpath runs through these woods and while it is possible to approach from the main roads I have included a recommended trailhead.
The last few meters are definitely not wheelchair accessible.