An attacker on Sunday threw firebombs at an immigration office used to process asylum seekers crossing the Channel in small boats and was later found dead.
The attack came as the government seeks to curb record arrivals.
Kent Police said that on Sunday morning "two or three incendiary devices" were thrown into a centre processing immigrants in the Channel port town of Dover in southern England, injuring two.
The BBC quoted the Home Office as saying the attack took part at the Western Jet Foil Border Force centre in the major Channel port town, used to process asylum seekers.
Police said the suspect had been "identified, and very quickly located at a nearby petrol station, and confirmed deceased".
They did not say how the individual had died, but Dover's Conservative MP Natalie told LBC Radio it was believed the "individual committed suicide".
Police also said two people "reported minor injuries inside the property".
The attacker had arrived at the scene in a car, they said, adding that another "device was found and confirmed safe" inside the vehicle.
Kent Live local news website posted photographs of police and fire services at the scene near the Port of Dover, and the BBC reported that a fire was put out.
- 'Tensions running high' -
Interior Minister Suella Braverman tweeted that there was a "distressing incident" and said she was "receiving regular updates on the situation".
"My thoughts are with those affected, the tireless Home Office staff and police responding," she added.
Elphicke tweeted: "I am deeply shocked by the incident in Dover today... My thoughts are with everyone involved."
The local MP said the attack took place at a centre where people arriving in small boats are initially taken before going to Manston, another processing centre in Kent.
The centre remains open but police said around 700 migrants were relocated to Manston during the initial phase of the investigation.
Elphicke told LBC: "We don't know the motivation of the individual concerned yet."
She added: "I think it is fair to say that tensions have been running high over the last period".
She cited a case where immigrants arriving in a small boat had entered a resident's home.
- Record figures -
Government figures showed that 990 migrants crossed the Channel in small boats on Saturday, bringing this year's record total to nearly 40,000.
The issue has caused a major political headache for the UK government, which promised tighter border controls after leaving the European Union.
Braverman has backed a plan for migrants crossing the Channel illegally to be sent to Rwanda, while this currently faces legal obstacles.
Elphicke wrote an article in the Mail on Sunday headlined: "When will the Left admit this is no refugee crisis... but simply illegal immigration".
UK Prime Minister Rishi Sunak said on Friday that in his first call in office with French President Emmanuel Macron the leaders agreed on greater cooperation to "deter deadly journeys across the Channel that benefit organised criminals".
Sunak has called for the Channel route to become "unviable" for people traffickers.
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© Agence France-Presse
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