Images of the warship - which weighs 65,000 tonnes, is 919ft (280m) long and currently alongside in Portsmouth - show a Multicat support boat called Uncle Bill at her stern.
The Sun newspaper revealed that a leaky seal around one of the propeller shafts was causing water to pour into the behemoth ship, an issue which is believed to have been known about for some time.
With a ladder visibly entering the water from the support boat on Tuesday, it is understood divers have been cleaning the ship and its huge propellers, which each weigh 33 tonnes.
A Royal Navy spokesman said the "repairs under contract are already under way alongside in Portsmouth", and the next round of sea trials will take place in the new year.
He said sea trials were "precisely for finding manageable teething problems like this and rectifying them", adding that the ship would continue to be "rigorously" tested before she entered service.
The warship, the biggest and most powerful built by the UK, was accepted into the Royal Navy fleet by the Queen earlier this month.
Defence Secretary, Gavin Williamson, insisted the repairs would not cost the British taxpayers a penny, with the bill to be covered by the contractors who built her.
It is understood the cost of fixing the leak will not cost millions as reported, but could reach into the hundreds of thousands.
During her estimated half-a-century working life, the vessel can be pressed into action for tasks such as high intensity war fighting or providing humanitarian aid and disaster relief.