Carte-de-Visite, studio Ernest Edwards in London

Assistant Surgeon, Royal Horse Artillery

This officer displays the badges of rank (crown and star on the collar) and cuff braiding characteristic of a Captain. Assistant Surgeons first ranked as Lieutenant, but would rank as Captain after 6 years service.

The detail of his medals isn't the best, but the looser suspender and longer ribbon of the central medal likely makes it a Turkish Crimean Medal - the left one would then be the British Crimean Medal. The Medal on the right is most likely an Indian Mutiny Medal (white ribbon with two red stripes).

Ernest Edwards operated at 20 Baker St. W. between 1864 and 1868.

A timeframe, a unit, a rank and some medals...more than enough to try to identify the gentleman !
And indeed, I could only find one officer sharing all those charcteristics, and he is likely Assistant-Surgeon Herbert Chalmers Miles, MD.

H.C. Miles was admitted a member of the Royal College of Surgeons at the meeting of the Court of Examiners on July 10 1854. His adress was then specified as "The Charterhouse".
He was gazetted Acting Assistant Surgeon on January 12 1855. He proceeded to the Crimea where he served in the Medical Staff (Medal and Clasp, and Turkish Medal). He came back to England on board the Calcutta steam transport, arriving from Constantinople and Smyrna on November 18 1855.
He joined the 83rd Regiment, with which he served in the Indian Campaign of 1857-58 ; he was present at the attack on Nimbkeira (severely wounded) ; during the defence of the fortified square of Neemuch in November 1857, altthough suffering from a gunshot wound, he served in medical charge of the detachment  of the 83rd Regiment and the wing of the 12th Native Infantry ; he was present during the field operations against Awah, and subsequent destruction of adjacent strongholds ; he served in medical charge of the 83rd Regiment prior to and was present during the siege operations against Kotah and its capture by assault (Medal and Clasp).
Assistant Surgeon Miles transferred to the Royal Artillery on June 24 1859. By 1862 he was attached to the 7th Brigade, and in October came back with it from Quebec on board the Himalaya, proceeding to Woolwich. On March 11 1863 he proceeded with the 7th Brigade from Woolwich to Portsmouth on board the iron steam troopship Maegera. By 1865 he had exchanged into the A Brigade Royal Horse Artillery.
On November 8 1867 he was promoted to Staff Surgeon. On June 23 1869, he was again appointed to the Regiment of Royal Artillery. The 1870 Army List states that he was then attached to the 6th Brigade.
The Times published on August 26th 1871 state that "Surg.-Major Miles, of the B Brigade", exchanged with Surgeon Franklyn, of the 1st Brigade.
An old piece of news - as he had died 2 months before (from "The British Medical Journal, August 5th, 1871) :

"OBITUARY.
HERBERT CHALMERS MIILES, L.R.C.P.ED.
RECENT intelligence from India brought to his family the painful intelligence of the death of Dr. Herbert Chalmers Mliles, Surgeon Royal Artillery, aged 38. He was the only surviving son of John Mliles, M.D., of Eastbourne, late of the Charterhouse. The deceased was educated at the Charterhouse School; and, after receiving his professional education at St. Bartholomew's Hospital, entered the army in 1854, and has since been in much active service. He was engaged during the Crimean war and during the Inidian mutiny, receiving a gun-shot wound at the siege of Neemuch, whilst under fire. He had the honour of being presented with three medals. After returning to England for some months, he was ordered to Nova Scotia, where he passed nearly two years. In December 1867, he was again ordered to India, where his short career terminated at Colaba, Bombay, on June 16th, I871, after twelve days of severe illness. He was buried with military honours at Sewree Cemetery, on June 17th. His funeral was attended by the Royal Artillery and many officers of the 49th and 19th Regiments, besides many friends."