Prime Minister David Cameron exits 10 Downing St. in London. TK

LONDON—The arrest of four men by British police on suspicion of terror-attack planning underscores how long-held fears are starting to be realized about foreign fighters returning from Syria to Europe to launch terrorist plots.

Police arrested the four individuals in London on Tuesday with assistance from armed officers as part of investigations into Islamist extremism in what the city’s top cop described as a “serious case.” The men remained in custody Wednesday for questioning, police said. None of the men had been charged as of Wednesday afternoon and searches were continuing.

London’s Metropolitan Police Service, known as Scotland Yard, said they used a Taser—a weapon that delivers an electric shock—on one of the suspects as he was being arrested. A person familiar with the matter identified that man as Tarik Hassane, who authorities believe has fought in Syria. A lawyer for Mr. Hassane couldn’t immediately be identified.

According to officials, the plot appeared to be related to Islamic extremism but was at the early stages and didn’t seem to be sophisticated in nature.

Authorities in the U.K. and elsewhere in Europe have over the past couple of years become increasingly concerned about the threat posed at home from foreign fighters returning from Syria. The concern is that those who return will be further radicalized and battle hardened.

The U.K. has recently secured a string of convictions regarding Syrian-related terrorist offenses. A total of six individuals as of early September had been convicted of crimes such as training in Syrian terror camps or assisting with terrorist funding, according to the Crown Prosecution Service. Now, the focus is starting to shift to potentially more serious cases where people are alleged to be plotting attacks.

In August, British authorities elevated the U.K.’s assessment of the level of the threat from international terrorism for the first time in three years. It was raised to “severe,” the second highest on its five-point scale that indicates an attack is “highly likely.” The increase was prompted, in part, by the increasing number of people returning to the U.K. after fighting in Syria and Iraq. At that time, British Prime Minister David Cameron said the threat from Islamic State “is a greater and deeper threat to our security than we have known before.”

The increased concern comes as Britain has recently begun participating in U.S.-led airstrikes against Islamic State in Iraq.

In making the case for U.K.’s involvement in the strikes, Mr. Cameron told his parliamentary colleagues last month that the first terrorist acts inspired by militant extremists Islamic State have already taken place in Europe, pointing to the recent charging of a French man suspected of killing four people at the Jewish Museum in Brussels in May. European authorities suspect the man, who has been charged with “murder in a terrorist context,” had fought with Islamic State militants in Syria.

Mr. Cameron, speaking in parliament, added that security services have disrupted six other plots in Europe.

In Australia, police last month carried out raids in two major cities, including Sydney, in a strike aimed at disrupting what they said were plans by local Islamic State supporters to behead members of the public.

One high-profile case involving an alleged terror plot is due to start Monday at London’s central criminal court, known as the Old Bailey.

The two defendants are Erol Incedal and Mounir Rarmoul-Bouhadjar, both aged 26 years and from London. Mr. Incedal faces charges in relation to preparing terrorist acts and Mr. Rarmoul-Bouhadjar is charged with possession of false identity documents. They have pleaded not guilty.

At least parts of the trial are expected to be subject to media-reporting restrictions. Under English law, which seeks to balance freedom of the press with the integrity of the judicial process, the media generally are prohibited from reporting material that could prejudice a jury.

British authorities have said some 500 people have gone from the U.K. to Syria and Iraq to fight, and about half of those have come back. While only a minority may become involved in planning terror attacks once back in the U.K., others may still assist the terrorist cause by spreading the jihadist message or assist with fundraising.

Following the arrest of the men in London on Tuesday, Metropolitan Police Commissioner Bernard Hogan-Howe said that the case confirmed the drumbeat around terrorism had intensified and the police needed to be more interventionist.

“And a lot of it is linked back to Syria and Iraq...these are arrests that in some way or other have got that sort of link,” said Mr. Hogan-Howe told the British Broadcasting Corp. “I don’t want to worry the people of London. We are here to keep them safe and we believe we are on top of things, but there are some concerns about the people we are having to arrest.”

—Nicholas Winning contributed to this article.

Write to Cassell Bryan-Low at