I think T = Territorial; confirmed by the six-digit number issued in March 1917 when all Territorials units were renumbered to reduce duplication.
510449 was in a block issued to Wessex Div Sig Company.
From 1914-1918.net:
Signals Company RE
In 1914 each infantry Division included a Signals Company with a total strength of 162 men. It was organised into a Company HQ and 4 Sections, of which No 1 Section was responsible for communications with Divisional HQ and Nos 2-4 with the Brigades of the Division.
Major or Captain in command of Company
4 Lieutenants (or Second Lieutenants), one each commanding a Section
25 other ranks at Company HQ (Company Sergeant-Major, Company Quartermaster Sergeant, 1 Sergeant at Company HQ, 1 Sergeant and 1 Corporal in Signallers Group, 1 Sergeant and 8 Corporal in Despatch Riders Group, 1 Shoeing Smith, 1 Trumpeter, 7 Drivers, 2 Batmen)
248 other ranks in No 1 Section (2 Sergeants, 2 Corporals, 3 2nd-Corporals, 1 Shoeing Smith, 26 Sappers, 12 Drivers, 2 Batmen)
72 other ranks in total in Nos 2-4 Sections (3 Sergeants, 3 2nd-Corporals, 24 Sappers and 6 Drivers in telephone sections; 3 Sergeants, 3 Corporals and 18 Sappers in signallers and despatch riders sections; 6 Batmen, 3 Sappers and 3 Drivers at Section HQs)
2 attached Privates of the Royal Army Medical Corps for water duties
1 attached Driver of the Army Service Corps (not counted into strength as officially he was part of the Divisional Train)
The Signals Companies relied on horses for transport and had an establishment of 33 riding horses plus 47 draught heavy and 4 pack horses. There were also 32 bicycles and 9 motorcycles.
With the exception of the Trumpeter, all other ranks were armed as infantrymen, carrying the SMLE rifle.
Ken