P&O Cruises’ Iona has 17 passenger decks, creating capacity for 5,200 holidaymakers before social distancing is taken into account.
She will be used by the operator for its summer season of domestic sailings.
Under a grey sky, the ship was greeted by a water salute as it sailed into Southampton on Sunday.
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The vessel is the first British liner fuelled by liquefied natural gas, which the operator described as “one of the cleanest fuels in the world”.
Ships of her size are normally powered by diesel engines which emit nitrogen oxides, affecting air quality.
Iona – 345 metres long (1,132ft) and weighing 185,000 tonnes – was built at the Meyer Werft shipyard in Papenburg, Germany.
She will sail on her maiden cruise to the Scottish island she was named after on August 7.
Sunday night’s naming ceremony will feature a performance by Take That star Gary Barlow, who is music director of an onboard entertainment venue.
The coronavirus pandemic means the event will be closed to the public but broadcast online.
Dame Irene Hays owner of travel agent Hays Travel, will be the ship’s godmother and will conduct proceedings.
P&O Cruises president Paul Ludlow said: ‘Since the inception of Hays Travel there is no-one who has been more supportive of cruising or been more of an ambassador for the travel industry than Dame Irene Hays.
‘As such there is no-one more appropriate to take centre stage on May 16 in this prestigious event as we celebrate her achievements and pay tribute to her husband John.’
John Hays, founder of the company, died suddenly aged 71 in November last year.
The first major sailing following Monday’s lifting of the ban on cruises in England will be operated by MSC Cruises.
Its ship Virtuosa will set off from Southampton for a four-night trip beginning on Thursday.
Cruises operating in England will only be allowed to carry up to 1,000 passengers – or 50 per cent of their capacity if that is lower – until all limits on social contact are removed.
Under Boris Johnson’s road map for easing restrictions, that was due to take place on June 21 at the earliest, but the Prime Minister has warned that the Indian coronavirus variant means his plan is in jeopardy.