The 1/8th Hants are directly connected to the PWRR (formed by the amalgamation of the QUEENS and R HAMPSHIRES). Their war history is in fact:
1/8th (Isle of Wight Rifles, "Princess Beatrice's") Battalion:
August 1914 : in Newport, Isle of Wight. April 1915 : attached to 163rd Brigade, 54th Division. Landed at Suvla Bay, Gallipoli on 9 August 1915. Left Gallipoli and moved to Egypt, arriving 19 December 1915. Moved into Palestine as part of EEF.
They were fairly unusual in this career, as most of the TF battalions in 43 Wessex Division served in India, Iraq and Afghanistan. Plus ca change eh?
The 1/25th Londons, originally the Cyclists' Battalion, served in India and fought in the Third Afghan War of 1919. There still is the London Regiment, a TA unit, which would have the closest hereditary links.