The sailor is alleged to have met the sex worker in a bar near the port of Kings Bay, Georgia, before taking back the payment as she dressed.
In addition, the crewmen are suspected of having organized drug parties while the submarine was docked in the USA; one of them is accused of having had sex with a prostitute in a pool. The female crew had been deployed on submarines three years ago.
The sub was docked in the USA to pick up nukes when tests were carried out, the Daily Mail reports.
They were identified as Commander Stuart Armstrong, 41, and Sub-Lieutenant Rebecca Edwards, 25.More news: DeMarcus Cousins says fan reception in Sacramento was 'beautiful'
The Daily Mail also revealed that the submarine's second-in-command, Lieutenant Commander Michael Seal, 36, has been removed over claims of an extra-marital affair with a 27-year-old female engineering officer who has also been taken off the sub.
All Royal Navy vessels have a "no touching rule" that prohibits intimate relationships on board.
Another crew member is reportedly facing court martial after going AWOL while two others are said to have quit.
The service personnel, stationed aboard HMS Vigilant - one of four Royal Navy submarines equipped with nuclear missiles - were dismissed after all tested positive for an illegal substance.
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