Cunard is a subsidiary of a company called Carnival. They are an American outfit based in New York.
If you work for an overseas employer or you work overseas for a UK employer, the tax you'll pay depends on where your employer's based, where you work and whether you're 'resident', 'ordinarily resident' or 'domiciled' in the UK.
If you're a UK resident seafarer and you spend long periods abroad, you may be able to claim 100 per cent relief, called 'Seafarers' Earnings Deduction'. It depends on how long you are considered to be outside of the UK in a single stretch and how often you're out in a tax year. It's not easy.
You may qualify for Seafarer's Earnings Deduction (SED) if you meet certain criteria. Any claims must be made in a Self-Assessment Tax Return. The Self-Assessment help sheet IR205 contains the conditions and a grid to calculate the days in and out of the UK in the claim period.
It is a complex process so you must get it right or it could cost you a lot of money.
If you telephone the HMRC or your local tax office (look in phone book) and they will send you a copy of this (5 page) document.