British Military Units found on the following pages of vol. 2 of Musgrave's Memoirs of the different rebellions in Ireland from the Arrival of the English, with a Particular Detail of that which broke out the 23rd of May, 1798. I will continue this practice as time allows:

p. 11: Lt.-col. Bainbridge, cmdr of the Durham Fencibles:

p. 12: County of Dublin Regiment; col. Vesey:

p. 15: 29th and the Queen's regiment

p. 19: Taghmen cavalry, cmdr. Cox

p. 33: North Cork regiment: Of possible use:
Mercer, J. Douglas. “Record of the North Cork Regiment of Militia, with sketches extracted from history of the times in which its services were required, from 1793 to 1880” 1886. 128 p. :
https://archive.org/details/recordofnorthcor00mercrich

p. 36-37: Wexford cavalry, cmdr.Capt. James Boyd.

p. 40: Queen's Regiment.

p. 44: Queen's Regiment.

p. 49: Queen's Regiment.

p. 50: Antrim militia [lt. Gardner], Hacketstown infantry [capt. Hardy]. 25th regt. [capt
Chamney], Talbots-town cavalry [capt. Hume], Shillelah cavalry [Lt. Braddell]; Atrim militia.

p. 52: Talbots-town cavalry [Lt. Fenton].

p. 53: Tinahely cavalry [capt. Hunter Gowan].

p. 54: Ancient Britons [col. Puleston]. 4th and 5th dragoons, the Ballaghkeene, Gorey and
Wingfield yeomany cavalry.

p. 55: Wingfield and Shillelah cavalry the Tinahely inft [capt. Morton, the Coolatin [capt.
Chamney and the Coolkenna [capt. Nixon] 120 total.

Some additions to:

Irish Rebels:
'Generals' Father John Murphy, father Kerns the priest, Anthony Perry, Edward Fitzgerald, and John Hay.
Esmond Kyan:
Priest Roche:
Edward Roche the lay general:
Keugh and Harvey

British:
Sir Ralph Abercromby (7 October 1734 – 28 March 1801): From 1797 to April 1798, he was
Commander-in-Chief of the forces in Ireland. "Command in Ireland 1797-1798" :
https://books.google.com/books?id=H0AJAAAAIAAJ&pg=PA61
Major General William Johnstone [Johnson]
Lt. General Gerard Lake (1744–1808):
Lt. General Ralph Dundas:
Lord Cornwallis:
Major General John Hely-Hutchinson:
Brigadier General Robert Taylor:
Lt. General Sir James Stuart:
Major General Trench:
General Knox:
General Hunter:
Major General Needham:
General Loftus:
General Moore:
Major General Sir James Duff:
Major General Wilford:
General Eustace
Generals Garret and William Byrne