A man, 27, and a woman, 26, were arrested at an address in Essex yesterday.
This followed the arrest of two men, aged 29 and 22, in Dover, Kent, on arrival from France on Monday. A quantity of ammunition was also seized.
Police searches of properties in east London and Lancashire are taking place, the BBC reported.
All four people are being held on suspicion of being involved in the commission, preparation or instigation of acts of terrorism under the Terrorism Act 2000, the report said.
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