No, the Cutty Sark was built in 1869 (IIRC) in Dunbarton, Scotland. Interestingly, she was built to carry tea as fast as possible from India and the far east and was the fastest sailing ship of her time, breaking many records. Unfortunately, the same year she was built, the Suez Canal opened making it easier and quicker to transport tea from India and could not be used by sailing ships, thus making the Cutty Sark somewhat redundant for her original role.
Dekker may have been thinking about the Victory or even the Mary Rose.
Yup...victory is older..by far :
HMS Victory HMS Victory stands today as the world's oldest commissioned warship. Still manned by Officers and Ratings of the Royal Navy, the Victory has seen over 220 years of almost continuous naval service.
Best known for her role in the Battle of Trafalgar, the Victory currently has a dual role as the flagship of the Commander-in-Chief Naval Home Command and as a living museum to the Georgian navy.
Launched in 1765 at Chatham Dockyard, the Victory was commissioned in 1778 and continued in active service for the next 34 years. In 1812 the Victory was retired from frontline duty and anchored in Portsmouth Harbour, on the south coast of England. For the next 110 years the Victory remained at her moorings in Portsmouth Harbour fulfilling a combination of practical and ceremonial roles.
In 1922, amid fears for her continued survival, the Victory was moved into Portsmouth's Royal Naval Dockyard and placed in No2 Dry Dock. Work then began on restoring the Victory to her 'fighting' 1805 condition.
Open to the public all year round, HMS Victory allows the visitor to explore the world of the Georgian navy, experiencing both the ship herself and the lives of the men who lived within her 'wooden world'.