Ariadne was the first paddle steamer to sail to the Channel Islands, arriving in St Helier Harbour, Jersey for the first time on the morning tide of June 9th 1824. She continued to provide a service linking the islands to the UK and France until 1846 and was scrapped three years later.
http://www.kingswearcastle.co.uk/Ariadne.htm

No evidence to support the poets assertions about Southampton's fame have been found

Spithead the sea between the isle of Wight and Portsmouth

According to Greek Myth Ariadne was the daughter of Minos-the King of Crete. She helped Theseus defeat the Minotaur by providing him with a sword; and with a ball of thread which he trailed behind him so that he could retrace his steps to escape the labyrinth. She thus became associated with weaving and spiders.