The 60 foot monument was built in 1864 to the memory of the medical officers of the British Army who fell in the Crimea War. It was situated near to where the cricket pavilion is today. It was demolished in 1973 due to it being in a dangerous state.
The names of the Medical Officers that were on the monument are on the following web site
Thanks to Randolph for pointing me in this direction.
The Officer's Mess was completed in 1867 and was built to accomodate the Officers who were visiting or worked in the hospital. It was converted into appartments in 1994 after being saved from demolition. It is now called Nightingale House, Nightingale Mews and Nightingale Walk and is a grade II listed building.