My apologies for my previous incomplete and misleading reply, I had only considered regular army regiments and neglected look-up details of the part-time volunteer and militia regiments; your response mentioning the “London Scottish” highlighted my omission.
After further checks there was a Volunteer Corps (St George's Hanover Square Volunteers) that had historically used the St. George & Dragon emblem and it continued to be used by its successor Corps.
The very large number of Volunteer Rifle Corps and the fact that as Rifle Corps many units wore their badges on the cross-belt (aka pouch-belts) rather than on their head-dress, there is no description in Kipling & King’s Head-Dress Badges of the British Army (Vol 1) of a badge associated with the St George's Hanover Square Volunteers or a successor Corps, until the post 1908 9th battalion of the London Regiment.
However I have found an image of a very fine example of the cross-belt badge of its successor the 11th Middlesex (St George’s) Rifle Volunteer Corps as worn 1860-1880; it’s just over halfway down the page at
http://www.victorianwars.com/viewtopic.php?f=19&t=9799 The St George’s emblem continued to be used by successor Corps within their helmet plates (e.g. 1st Middlesex (Victoria and St Georges) Rifle Volunteer Corps), see
http://www.britisharmybadges.com/shop.php?c=2 3rd image down; that badge is very similar to that of the 9th Battalion, The London Regiment of 1908 described in Kipling & King.
Using the name and dates you gave a search of the London Gazette at
https://www.thegazette.co.uk/ (not very user friendly) revealed:
London Gazette 28 November 1879, Issue 24787, page 6943
11th Middlesex Corps, Frederick William Mortimer, Gent, to be Second Lieutenant (Supernumerary). Dated 29th November 1879.
London Gazette 4 January 1881, Issue 24920, page 4
6th (late 11th) Middlesex Corps, Second Lieutenant Frederick William Mortimer to be Lieutenant.
London Gazette 12 May 1885, Issue 24569, page 2163
Rifle, 6th Middlesex (St George’s) Lieutenant Frederick William Mortimer to be Captain, Dated 13 May 1885.
London Gazette 27 May 1892, Issue 26292, page 3144
6th Middlesex (St George’s), Captain F. W. Mortimer resigns his Commission. Dated 28th May 1892
You can now see why infosending requested the information about the writing on the stick.
I don’t believe any Volunteer Corps served in the 1st Anglo Boer War (1880-1881) and as he resigned his Commission in 1892, it’s unlikely he took up service with them in the 2nd Anglo Boer War (1899-1902). You should search the British Army Medal Rolls on Ancestry to see if he ever served in South Africa.
If you mentioned the Boer War because you have been unable to find him in the 1901 Census, there is a notice in a 1900 London Gazette about the estate of a Frederick William Mortimer who died 2nd August 1900.
London Gazette 16 October 1900, Issue 27238, page 6375.
I’ve added this background to show the previous Corps titles.
The London Scottish was originally raised in 1859 with the name the London Scottish Rifle Volunteer Corps, in 1860 it was renamed the 15th Middlesex (London Scottish) Rifle Volunteer Corps and in September 1880 was renumbered the 7th Middlesex (London Scottish) Rifle Volunteer Corps.
Also in 1859 another Rifle Volunteer Corps was raised in the Parish of St George Hanover Square and based on the original 1794 antecedent regiment (St George's Hanover Square Volunteers) it was named St George’s Rifles, 11th Middlesex Rifle Volunteer Corps, a year later it was renamed the 11th Middlesex (St George’s) Rifle Volunteer Corps, in September 1880 it became the 6th Middlesex (St Georges) Rifle Volunteer Corps.
In June 1892 the Corps was amalgamated with the 1st Middlesex (Victoria) Rifle Volunteer Corps to become the 1st Middlesex (Victoria and St Georges) Rifle Volunteer Corps.
To complete the picture of these two VRC’s.
When the Territorial Force was created in 1908 as both the above two Corps came within the boundary of the County of London (est. 1889), they became the 14th (County of London) Battalion, The London Regiment (London Scottish) and the 9th (County of London) Battalion, The London Regiment (Queen Victoria’s Rifles).