The Britannia was a whaler with a crew of 24 men. She was 301 tons, had six guns and was built in Bridport in 1784. The Britannia and the Speedy were both owned by Samuel Enderby & Sons......
In 1792 Samuel Enderby and Sons, under the auspices and direction of the Lords of the Admiralty sent Lieut. James Colnett R.N., in the whale ship Rattler, to the Pacific Ocean. There he found great numbers of sperm whales at the Galapagos Islands, which are situated on the equator. In 1793 the Northern Pacific, to the east of 180° was opened to the vessels of the Southern Whale Fishery. In a letter dated in November 1797, Samuel Enderby and Sons wrote:
"The Pacific Ocean abounding with spermaceti whales all adventurers who can afford to venture the risque of so large a speculation send their vessels into those seas, where we consider them safer from the enemy (France and Spain) than in any other part of the Ocean where sperm whales are found. It is impossible a vessel can go there an return without going into some port to refresh..."
"The writers, who had a vessel almost ready to sail for the fishery, therefore sought a contract to carry female convicts to New South Wales where they proposed to give the fishery on that coast a fair trial." 
The Britannia arrived in Portsmouth on 10 January 1798 to begin embarking the female convicts. The women had been convicted in districts throughout England - in Surrey, Lancaster, London, Kent, Essex, Liverpool, Devonshire, Westminster, Hereford, Bristol, Somerset, Horsham and Warwick. The youngest was Sarah Johnson who was tried at the Old Bailey and found guilty of feloniously stealing, on the 19th of October, a linen shirt, value 6s. a linen shift, value 2s., a check linen apron, value 10d., a black silk bonnet, value 3s. and a scarlet cloth cloak, value 6d., the property of Philip Baldwin.
Sarah Johnson was sentenced to 7 years transportation as were most of the women. Only seven women had been sentenced to transportation for life - Mary Brown, Mary Cole, Martha Edwards, Mary Hodges, Elizabeth Hulme, Elizabeth O'Connor and Ann Tracey.
Ann Tracey and Mary Brown's crime was reported in the London Sun on 7th December 1797.... Ann Tracey, Peter Tracey her son, a boy of about ten and Mary Brown were tried for robbing William Witnell of a holland apron, a hat, and other articles. The substance of the evidence was this - the Prosecutor, on Lord Mayor's Day, meeting the prisoners Brown, was seduced by her to prisoner Ann Tracey's who kept a house of ill fame on Saltpetre Bank. The Prosecutor who said he had drank rather freely, but was not so intoxicated as to loose his reason or recollection, sent for some liquor; while they were were drinking it the prisoners seized an opportunity to commit the robbery. The two female prisoners aided by several other women, attacked him with a fire shovel and other weapons, while the boy, from behind struck him a violent blow with a poker, that stunned and much cut him. by the assistance of three Peace Officers whom he called in, the prisoners were conveyed to the watch house. The prisoners said a few words in their defence but called no witnesses. Mr. Justice Grose summoned up with his accustomed ability. All the prisoners were returned guilty; but the boy on account of his youth was recommended to mercy.
The Britannia departed Portsmouth on 17 February 1798 with ninety-six female convicts and was supposed to have on board provisions for nine months after their arrival. Two women died on the voyage out.
The Britannia arrived in Port Jackson on 18 July 1798.
According to David Collins, July 1798 was uncommonly cold and sharp frosts were experienced every night in the interior districts.
STATE OF THE COLONY
The loss of the Lady Shore with her provisions for the colony was a severe blow. Governor Hunter reported their desperate needs to the Duke of Portland when the Britannia arrived without the much needed provisions:
Governor Hunter to the Duke of Portland,
Sydney 25th September 1798.
It is also a subject of great regret to me my Lord, to be under the necessity of mentioning the destitute state of our public stores in regard to slops of every kind and of bedding. The loss of the Lady Shore, transport, and the very few supplies of this nature brought lately into the colony, have so impoverished us that the people are, literally speaking nearly naked, and great numbers without a bed or blanket to lie upon. Your Grace will excuse my being very earnest in recommending this subject as a matter requiring the earliest attention. Anxious to give every possible encouragement to the rearing of swine, I have lately taken more pork into store than formerly. I have therefore only to request my Lord, that this circumstance be consider'd when bills appear as it must be paid for here. The provision mentioned in your Grace's letter by the Britannia, which was to have been landed with the female convicts she brought here, had not been put on board that ship. All that was landed here was what remained of the sea victualling. 
The longed-for provisions had not arrived on the Britannia, however the contingent of females perhaps softened the blow and according to David Collins in An Account of the English Colony they were much sought after...... Previous to their departure, the Argo, a small Amereican schooner, arrived, last from the Isle of France, having on board a cargo of salt provisions, some French brandy, and other articles, upon speculation; and on the 18th arrived the Britannia whaler from England with 94 female convicts. The cattle that came in the Hunter, and which were sold by auction about the same time, were not greater objects of contest than were these ladies, the number of women in the settlements bearing no proportion to the men.
There seems to have been no government accommodation for female prisoners in 1798. The Female Factory at Parramatta had yet to be established and the women of the Britannia were likely distributed amongst the free population.
After disembarking her prisoners, the Britannia departed for the south sea whale fisheries. The Historical Records of Australia Vol., p. 571 records the Britannia, Captain Robert Turnbull arriving in Port Jackson having returned from the fisheries on 4th November 1799 with 160 tons of spermaceti oil.
NOTES AND LINKS
1). Mary Hyde arrived as a convict on the Britannia. She later entered a relationship with John Black and as a widow in 1814 married Simeon Lord. Together they became one of the richest couples in the colony. (Wikipedia)
2). In 1810 the following people who had arrived on the Britannia received their Certificates of Freedom being restored to all the Rights of Free Subjects in consequence of their terms of transportation being expired... Sarah Leather, Elizabeth Lewis, Anne Wood, Elizabeth Kelsall, Letitia Baker.
3). Letitia Baker signified her intention to depart the colony on the Anne in May 1819 (Sydney Gazette)
4). Ann Dillon arrived as a convict on the Britannia. She died in February 1804 and was buried in the Old Sydney Burial Ground
5). Departure of the whaler Britannia from Sydney Cove in 1798 by Thomas Whitcombe
6). More about Samuel Enderby and the whaling industry at Australian Dictionary of Biography Online
. Sun (London, England), Monday, December 7, 1795; Issue 997.
. The Proceedings of the Old Bailey Online
. Shipping Arrivals & Departures, Sydney 1788 - 1825 by John Stanley Cumpston. p. 7
. HR NSW, Vol., III p493