Hugh Walker was entered in the Navy List of Medical Officers in 1814. 
Hugh Walker was employed as surgeon superintendent on two convict ship voyages to Australia and another voyage bringing passengers and troops:
1). Guildford convict ship departed Portsmouth on 14 May 1820 ; arrived in Port Jackson on 30 September 1820. He returned to England on the Guildford in October 1820. Surgeons Robert Espie and Thomas Reid also returned to England on the Guildford.
2). Jupiter with passengers and troops arriving in Hobart in 1823. He returned to England on the Ocean in February 1824.
3). Minstrel convict ship departed Portsmouth 17 April 1825; arrived Port Jackson on 22 August 1825.
On 26 May 1827 Hugh Walker embarked on the ill-fated voyage of the Cumberland, Captain Carns, bound for England. 
Passengers included Mr. W. Emmett and two children, Commissary William Clements; Mr. W.O. Vallance; Mr. Mead; and Peter Robinson.
The Cumberland was never heard from again and for some time it was thought she had foundered at sea however evidence emerged that suggested she had been taken by pirates and all on board including Hugh Walker, barbarously murdered.
The story of the Cumberland was told in The History of Tasmania by John West......
When no tidings were heard of the Cumberland, it was supposed she had foundered; but in the year 1828, Captain Duthie, of the Bengal Merchant, threw light on her fate. He had found the Clarinda, Captain Crew, at Rio, who had been boarded in lat. 8° S. The pirates chained him to the deck while they robbed the vessel: he saw a bucket, on which he could trace the word Cumberland. Some of the pirates proposed that Crew should walk the plank, but were resisted by the Captain.
A little black boy, shipped by the Clarinda at the Cape de Verde Island, remembered the pirate vessel as often seen in that port. In what form the Cumberland perished is not certainly known. Pirates executed in England for other crimes, were supposed to be guilty of this: more than a hundred and fifty persons perished by their violence. Some they cut down, and others they cast overboard. They were driven to the Sort of Cadiz by a storm, and attempting to negotiate a bill they were detected.
A ship of war conveyed them to Gibraltar, where several suffered; others were forwarded to England, and condemned there. The story of the capture was long a standing topic in the unarmed merchantmen that passed her track.
As the emigrant, even now, approaches the supposed latitude, he hears with bated breath the fate of the Cumberland, whenever a strange sail darkens the horizon. 
Memorial to Hugh Walker
'Sacred to the Memory of Hugh Walker, Esq., Surgeon R.N., aged 52 of Larne, in the County of Antrim in Ireland, who on his return from a third voyage to New South Wales found his beloved Wife and (only) child deposited in the Family Vault beneath as Commemorated on the adjoining Monument, in deep affliction and agony of mind undertook his fourth voyage to that Country, from whence returning in the Ship Cumberland of London in the Month of May 1827, he together with the Captain (Carne) the whole Crew and all the Passengers are believed to have perished at Sea in the South Pacific Ocean. A small vestige of the Ship only was discovered giving too melancholy a proof of the afflictive nature of the event.
'Sacred to the Memory of Catherine wife of Hugh Walker, Esqr. Surgeon R N and Daughter of the late Thos. Darracott, Esqr, an Alderman of this Town, who died 12th September 1825, aged 51 Years, Also of Thomas Samuel their Son who Died 3rd May, 1826, aged 10 Years. Their Mortal Remains are deposited in the Family Vault of the Darracotts the Entrance to which, is close on the Inside of the Southern Door of this Church.' 
Notes and Links
William Clements who perished on the voyage of the Cumberland was the same man who came up against one of Australia's most famous bushrangers - Bold Jack Donohoe. Read more about his encouter here.
The Sydney Gazette relayed how it came to be that William Clements was a passenger on the Cumberland.....It may be remembered that William Clements was shot at by bushrangers, near Liverpool, on the Christmas day of 1826, by which he totally lost one eye, and almost the sight of the other. He was for some time in a most dangerous state; and when he had sufficiently recovered, it being considered that he was forever incapacitated for business, it was thought advisable that he should return to his native land. He was a most amiable young man, and his hapless fate must excite, in every feeling breast, a deeply melancholy interest.