A video posted on social media appears to show Daniel Thomas, 37, taking a knife to an inflatable boat, which was empty of migrants but had a rescue services member aboard, while shouting, "You're in English territory".
Hampshire and Isle of Wight Constabulary said a 37-year-old man was arrested on Wednesday evening on suspicion of criminal damage with intent to endanger life and endangering the safety of a vessel.
It said he remained in custody on Thursday.
British police do not identify suspects by name until they are charged.
Thomas, who goes by the nickname Danny Tommo, is a longtime associate of far-right activist Stephen Yaxley-Lennon, also known as Tommy Robinson.
Patriot Platform, a group Thomas founded, is behind recent protests in which masked, black-clad men tried to stop migrants reaching the UK.
Earlier in September, masked demonstrators blocked the port of Dover, in southeast England, and tried to stop migrants being taken ashore in Portsmouth on the country's south coast.
Successive UK governments have struggled to stop people - more than 41,000 in 2025 - making the dangerous journey across one of the world's busiest shipping lanes.
The issue has been depicted as a crisis by politicians including Nigel Farage of the hard-right party Reform UK, and has been used as a rallying point by anti-immigration activists.
Prime Minister Andy Burnham's centre-left government says stepped-up law enforcement co-operation between Britain and France has helped reduce the number of people making the crossing so far in 2026 by more than 40 per cent compared with 2025.
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