In the Church of England Hymn Book, "Jesus Came, Heavens Adoring" is Hymn number 300, not "Bread of Heaven".
Although Lady Godiva is a famous figure from English folklore, the roots of the legend are believed to be from pagan mythology. It, therefore, seems exceptionally unlikely that she would be featured in a Church Of England ceremony in gross violation of doctrine.
Only in Scotland are vicars imposed by the Bishop. In England, Church Of England vicars must be "elected". In short, a new vicar is only ever offered for approval. If they are not positively approved by the congregation, they cannot be installed in the first place. Actually, the Dibley Parish Council DO vote to have Geraldine as vicar.
During the 'Cwm Rhondda' hymn, it flicks through a series of images showing Dibley village. In one, a car can clearly be seen travelling backwards, as the film has obviously been reversed.
As Summer Solstice celebrations are regarded as pagan, the Church Of England specifically never holds a ceremony to celebrate it.
The vicar announces that after the sermon, the congregation will sing hymn 300. But the two last numbers on the hymn board are 214 and 75. Even if the sermon was followed by a hymn and closing prayers and blessing and a recessional hymn, the numbers on the hymn board do not match the announcement.
David claims that it would be difficult to find anyone older than Reverend Pottle without recruiting a member of The Rolling Stones, but Mick Jagger was still only 51 at the time that this episode aired.
Crossing ones fingers is considered to be an occult and superstitious practice by the Church Of England, hence it would be wholly unlikely that a Church Of England vicar would do this in violation of fundamental doctrine.