Three men and a woman were detained in Birmingham and another man was held at London’s Gatwick Airport in the early hours of yesterday.
Chief Constable Marcus Beale from West Midlands Police said there was no information to suggest an attack in Britain was being planned.
He added in a statement: “This action forms part of an extensive investigation by West Midlands Counter Terrorism Unit, together with the wider counter terrorism network, [domestic spy agency] MI5 and international partners including Belgian and French authorities to address any associated threat to the UK following the attacks in mainland Europe.”
Police declined to give any further details but a security source confirmed the arrests were linked to the suicide bombings in Brussels which killed 32 people last month and November’s attacks in Paris, which left 130 people dead.
The four men, aged 40, 59 and two aged 26, and the 29-year-old woman are now being questioned by counter-terrorism detectives and police are searching several properties in Birmingham.
British media have reported that Belgian Mohamed Abrini, suspected of involvement in the Islamic State attacks in Brussels, had travelled to Birmingham last year and taken photos of a soccer stadium.
Abrini, who investigators say has confessed to leaving a bomb at Brussels airport, is also wanted in connection with the Paris attacks.
Abdelhamid Abaaoud, the suspected planner of the Paris attacks who was killed by French police late last year, is also reported by British newspapers to have visited Birmingham last October and had photographs of places in the city on his smartphone.
Asked about Abaaoud in parliament last month, home secretary Theresa May said: “This is obviously an ongoing investigation, and we are working very closely with the Belgian authorities to ascertain as much information as possible about the individuals involved.”
Meanwhile, French police have targeted hundreds of websites suspected of “inciting or glorifying acts of terrorism” after the Paris attacks by ordering content removals, delisting sites from search engines or blocking access.
The French privacy watchdog in charge of monitoring website closures said more than 1,000 pieces of web content have been removed, nearly 400 URLs ordered delisted and 68 websites blocked since November.
Alexandre Linden, the privacy commission’s ombudsman, said that he approved all the requested web closures except one — a photograph of dozens of people killed by attackers inside the Bataclan.
Mr Linden said the photograph’s context meant it was not “inciting or glorifying terrorism” and the Interior Ministry agreed to reverse its decision.
The Islamic State fighters who carried out the attacks in Brussels honed their skills through combat in Syria, and the sibling suicide bombers were also crucial to planning the Paris attacks, according to the extremist group’s magazine.
In the English-language magazine Dabiq, the group drew a direct line between the two attacks — and made no mention of the key suspects captured in Belgium. “All preparations for the raids in Paris and Brussels started with” brothers Khalid and Ibrahim El-Bakraoui, the group said.
Brussels was home to many of the attackers who struck Paris on November 13 with suicide bombings and volleys of assault weapons fire that left 130 people dead.
According to Belgian and French investigators, the same cell was behind the suicide bombings that killed 32 people in Brussels on March 22.