This is Lodington, rather than Day related but I just found this whilst looking into the Berkeley family of Biggin Hall, Benefield (a parish the Broades and Lodingtons resided in at one time):
(Page 12)
Marriages solemnized in the parish of Greenwich in the County of Kent in the year 1797.
Charles Berkeley of the parish of Oundle in the County of Northampton and Charles Elizabeth Munn of this Parish were married in this Church by license this twenty ninth day of March in the year One Thousand seven hundred & ninety seven
by me J Lodington Preb: of Lincoln.
This Marriage was solemnized between us
Chas. Berkeley
Charlotte Elizth. Munn.
In the presence of
James Munn,
Paul Sandby Munn
Sarah Maria Best,
Catherine Anne Best.
The above is a true extract from the Register of Marriages belonging to the Parish Church of Greenwich, in the County of Kent, taken this 9th. day of Jany 1850
By me R.R.P.Stanley. Curate
One of Charles Berkeley, of Biggin Hall, Benefield and Charles Elizabeth Munn's children was Anne Maria Berkeley. She married Rev. Henry Good, LL.B., vicar of Royal Collegiate Church of Wimborne Minster, Dorset.
Rev. Henry Good, LL.B's parents were Rev. Henry Good, M.A., rector of Stockton, Wiltshire and Eleanor Hiley.
The parents of the Rev. Henry Good, M.A. were Rev. Henry Good, D.D., rector of Shroton and Cann St. Rumbold, Dorset and Ann Smith.
This Ann Smith was his second wife. His first wife was Eleanor Smith (probably her sister), daughter of Rev. Peter Smith, M.A., B.A., rector of Melbury Abbas, Dorset and Joanna.
Her brother was John Smith, of Bucklersbury, London. Thus we get back to the Lodingtons again.
The J. Lodington mentioned above happens to be Rev. Joseph Lodington, Prebendary of Lincoln and one time vicar of Oundle, Northamptonshire. He died in Benefield in December 1806. His mother was of the Broade family, whose father and brother were rectors of Benefield.
So he definitely knew the Berkeley family, also of Benefield. His wife also happened to be Joanna Maria Smith, daughter of John Smith, of Bucklersbury, London.
I suspect there maybe other links too. I shall see of I can find some.