The two church parishes of Market Lavington and Easterton have separate identities but in 1962 they were merged into one benefice.
This document, published by HMSO, explains.

Document setting out the formation of the combined benefice of Market Lavington and Easterton
It looks as though this document has been used as a drink coaster at some point in the past so let’s transcribe this legal document.
AT THE COURT AT BUCKINGHAM PALACE
The 28th day of November, 1962
Present.
THE QUEEN’S MOST EXCELLENT MAJESTY IN COUNCIL
Whereas the Church Commissioners have duly prepared and laid before Her Majesty in Council a Scheme bearing date the 14th day of November, 1962. in the words and figures following, that is to say:
“We, the Church Commissioners, acting in pursuance of the Pastoral Reorganisation Measure, 1949, and the Union of Benefices Measures, 1923 to 1952, now humbly lay before Your Majesty in Council the following Scheme which we have prepared with the consent of the Right Reverend William, Bishop of Salisbury, (in witness whereof e-has signed the Scheme)
for effecting the union of the benefice of Market Lavington and the benefice of Easterton, both situate in the diocese of Salisbury.
“SCHEME
“1. Union of Benefices. The benefice of Market Lavington and the benefice of Easterton shall be permanently united together and form one benefice with cure of souls under the style of ‘The United Benefice of Market Lavington and Easterton’ but the parishes of the said benefices shall continue in all respects distinct.
“2. Taking effect of union. Upon the day when notice of the making of any Order of Your Majesty in Council affirming this Scheme is published in the London Gazette the union shall forthwith take effect.
“3. Patronage. After the union has taken effect the right of presentation to the united benefice shall be exercised by the patrons of the two benefices alternately, the patron of the benefice of Easterton having the first presentation to the-united benefice to be made after the union.”
And whereas the provisions of the Union of Benefices Measures, 1923 to 1952, the Union of Benefices Rules, 1926 and 1930, and the Pastoral Reorganisation Measure, 1949, relating to the preparation and submission of this Scheme have been duly complied with:
And whereas the said ‘Scheme has been approved by Her Majesty in Council:
Now, therefore, Her Majesty, by and with the advice of Her said Council, is pleased hereby to affirm the said Scheme and to order that it shall be and become effectual in law immediately upon the publication of notice of the making of this Order in the London Gazette.
W. G. Agnew.
The main effect was to be a shared Vicar. The next Rector that this area gets will have to serve five parishes.