I came across this report of the unveiling of the memorial tablet, not in the church, but in Penny Bridge School. The school is still in the original building, so it's not obvious why the tablet was later moved.
It's noticeable that there's no mention of any relations of Private Wilson being present at the unveiling; perhaps they'd moved away from the area.
MEMORIAL
TABLET AT
PENNY
BRIDGE
SCHOOL
. - A tablet was unveiled by Mrs. Machell, of Penny Bridge Hall, on Saturday afternoon. The Rev. C. G. Townley presided, the schoolroom being quite full. Amongst those present were Major and Mrs. Machell, Captain Burton, Mrs. Clarke, Summerhill; Mrs. Woodburne, Thurstonville; Dr. and Mrs. Long, Mrs. Huddleston, Mrs. Stanley, Mrs. Townley, Miss Burrows, Miss Fell, Sergt. Telpts, the Rev. J. P. Airey, and others. The scholars opened the proceedings by singing "O England, O my country." The Rev. C. G. Townley made a few remarks; then followed the children's song, "The Brave Comrade." Mrs. Machell then said: "I unveil this tablet in memory of William Anderton Wilson, private in the 2nd Battalion The King's Own Royal Lancaster Regiment, who was killed in action near Ladysmith, Feb. 22nd 1900. A former pupil of Penny Bridge School." Untying the ribbon, the curtain automatically removed. "God save the Queen" was then heartily rendered. Mr. W. White then read letters from the Commander-in-Chief, one from the newly-appointed vicar, the Rev. O. Rhodes, and one from Col. Murray, commanding the 4th Regimental District, and others. Mr. White, as originator of the movement, acknowledged the help of the committee of his former pupils, schoolfellows of the late private, and the invaluable assistance of Mr. J. P. Taylor and other helpers. After the infants' Flag Song, Mr. J. P. Taylor, as chairman of the committee, said: "On behalf of the committee and subscribers I give in trust for ever this tablet to the managers of Penny Bridge School." The scholars then sang "Union Jack," after which Capt. Burton said he attended by command of Col. Murray. The ceremony that day was a credit to all who had taken part in it. He gave an interesting history of the King's Own. After a further song, "For Queen and Country," by George Stanley and T. Keen, the Rev. J. P. Airey moved a vote of thanks to Mrs. Machell for the gracious manner in which she had performed the ceremony. Major Machell suitably responded on behalf of his wife. "Rule Britannia" was then sung and a vote of thanks accorded to the Rev. C. G. Townley for presiding.
(Westmorland Gazette, 17 November 1900)