The young man in his 20s was assaulted by someone reportedly watching the small boat arrive at the village of Kingsdown, south of Deal, on Sunday.
Natalie Elphicke – the Conservative MP for Dover & Deal who has called for migrant boats to be “stopped and returned” – condemned the violence and warned against “vigilante behaviour”.
Kent Police said officers were now searching for the person who attacked the migrant, who was not badly hurt.
“Kent Police were notified at around 11.05am on Sunday of a reported assault of a man in his 20s off Undercliffe Road, Kingsdown,” said a spokesperson.
“Officers attended to ensure the welfare of the man, who was not seriously injured and did not require hospital treatment. Inquiries to establish the circumstances surrounding the incident and the identity of the person responsible are ongoing.”
Ms Elphicke said: “While urgent action is needed by the French and the Home Office, there is no excuse for violence or vigilante behaviour.”
The local Tory MP was criticised for rhetoric used during a video message she tweeted on Sunday after watching eight migrants come ashore at Cliffe. She stated: “This is unacceptable that people are breaking into Britain in this way.”
Immigration and family law barrister Andrew Powell condemned Ms Elphicke’s “appalling and dehumanising language”.
There is no lawful restriction against people choosing the country in which they want to seek asylum, and the people crossing the Channel are not committing any unlawful act in doing so, according to Christopher Desira, human rights and immigration solicitor at Seraphus law firm.
Kent County Council has said it cannot provide any care for any more unaccompanied asylum-seeking children because it had reached “capacity”, and they are now being held in a migrant "processing" centre.
Council leader Roger Gough said on Monday the he had informed the Home Office his local authority was “expected to reach safe capacity to meet its statutory duty of care this weekend” after 13 more children arrived over the weekend.
“That is clearly unacceptable and needs to be resolved immediately,” said Kent Refugee Action Network, a group supporting hundreds of migrant children.
Bridget Chapman, a caseworker for the group, said: “We don’t tend to ask too many direct questions about where people have come from and why they’ve come because obviously the reasons can be traumatic.
Many of the young people arriving in Kent on dinghies are Kurdish and have come from Iraq and Iran, she said. “Any information we’ve got is information that people have chosen to share with us and it’s not comprehensive.”