It was welcomed by Yemeni Trade Minister Abdul-Rahman Mohammad Ali Othman and Britain's ambassador to Yemen. It is to host a symposium entitled "Invest in Yemen", which has been proclaimed by the local press as a "milestone in Yemeni-UK business".
Representatives of British Petroleum, British Airways, British Aerospace and General Electric will attend. Britain is Yemen's second-largest trading partner after the United States.
But there is a deeper symbolism behind the visit, as Britain and Yemen dust off relations after 30 years of tension. Aden was taken by the British in 1831, another in the series of ports and coaling stations that helped knit together the nascent empire.
Britain ruled both Aden and the surrounding territories, which were held as a protectorate. Many Yemenis have settled in Britain, especially around London, Liverpool, South Wales and Sheffield.
But a violent and bloody insurgency led London to evacuate in 1967, leaving Britain's remaining ambitions east of Suez in tatters.
Aden and the "South Arabian Federation" became the Peoples' Democratic Republic of Yemen (South Yemen), a Soviet satrap; this, in turn, was absorbed in a merger with the neighbouring Yemen Arab Republic (North Yemen) in 1991, to form what is now Yemen, an impoverished small oil-producer country with 16 million people.
In the interim, Britain financed and assisted insurgencies in both South and North, leading many in both Aden and San'a (capital of the north) to see London as the continuing imperial enemy.
Now Britain is keen to restore relations, in particular because British oil companies have a stake in the country's oil fields. British Airways flies to Aden and San'a once again. Malcolm Rifkind, the Foreign Secretary, visited Aden last year, the first Cabinet minister to do so for 30 years. Pride of place in his office is taken by a traditional Yemeni curved silver knife.
Ironically, the last time that Britannia was moored off the Yemeni coast, it was evacuating British nationals from the South during the disastrous and bloody 1986 civil war. It was one of the few occasions when Britannia has shown her use.
But after Aden, the days of the vessel, like the vestigial British Empire, are numbered. Britannia is due to leave Yemen on Sunday and head to the Gulf, where it will make visits to the United Arab Emirates, Qatar, Kuwait and Bahrain.
From there, it heads off to Asia, to take Governor Chris Patten, Prince Charles and the Foreign Secretary of the day away from Hong Kong after the Union flag is hauled down.