NO - you will be ok without adaptor on the SPirit - and for that matter the Celebration too but not on the Destiny. My wife has used her 240V GHDs on the first two ships above in our cabins. As for the Destiny you have to use a special plug out in the corridor !!!! We have sailed on all 3 ships in the last 2 years.
I could not use my hair straightners with an adaptor as it was an american ship and to do with voltage, but my mobile phone worked. Would think if an english ship will be an english type plug and shouldn't be a problem?
You will need an adaptor, as the Spirit has continental sockets. The voltage is 110 and 220v. It may be worth buying some travel/multi voltage straighteners as I did (Argos - less than £20!) which are guaranteed to work from 110volts. I overheard one lady complaining that hers wouldn't heat up, and so she had to buy some specially in one of the ports!