A sketch made Monday by a court artist of Erol Incedal, center, at the Central Criminal Court "Old Bailey" London. Associated Press

LONDON—A British man being tried here on terror charges was considering a massacre on the scale of the 2008 attack in Mumbai, and had former Prime Minister Tony Blair ’s home address, prosecutors said Tuesday.

Erol Incedal, a 26-year old south Londoner, also had shown a keen interest in the militant group Islamic State, prosecutors said on the first day of arguments in his high-profile trial.

The case is one of the first in the U.K. involving an alleged terrorist plot and the civil war in Syria, although British prosecutors have recently secured convictions for lesser offenses such as training in Syrian terror camps or assisting with terrorist funding.

Mr. Incedal, who is of Turkish origin, faces one charge of preparing terrorist acts and another of possessing bomb-making instructions. He denies both charges.

Mr. Incedal’s co-defendant, Mounir Rarmoul-Bouhadjar, also 26 and from south London, last week pleaded guilty to possessing a terrorist document, prosecutors told the jury Tuesday.

Richard Whittam, the lead prosecutor, said in his opening statement that Mr. Incedal was plotting an act of terrorism against “an individual of significance, or a more wide-ranging and indiscriminate attack.”

In September 2013, police pulled Mr. Incedal over for an alleged traffic violation. Police searched the black Mercedes he was driving and found a white Versace glasses case containing a piece of paper with Mr. Blair’s address on it, Mr. Whittam told the court.

Mr. Whittam said police also discovered a notebook with a handwritten note: “Oh you, the believers, fight those of the infidel who are near to you. Why do you not fight in Allah’s cause for those oppressed men, women and children who cry out: ’Rescue us from this town.’ ”

While searching the car, police planted a listening device and later heard Mr. Incedal discussing the need to find a safe house to stash sensitive material, Mr. Whittam alleged.

Two weeks later, police arrested Messrs. Incedal and Rarmoul-Bouhadjar on a busy road near the Tower of London after shooting out the tires of a black Mercedes driven by Mr. Incedal.

Mr. Whittam said that an examination of Mr. Incedal’s iPhone following the arrests showed he had searched on the Internet for videos of Islamic State of Iraq and al-Sham—a historic geography spanning the Levant—known as ISIS. Mr. Incedal had also chosen the movement’s black flag as his phone screen saver, the court heard.

A laptop belonging to Mr. Incedal also showed the creation of a Skype account in the name of a woman, Fatima Hamoodi, that was used to communicate with another user, Zaynab Alawii, according to Mr. Whittam. The prosecutor didn’t say whether they were pseudonyms.

Mr. Whittam told jurors that they would be shown evidence suggesting the two people using the accounts made coded references to staging a commando-style attack similar to the one in Mumbai that resulted in the death of more than 160 people.

One reference to “mo88m ssbaay style” could be taken to refer to the attack by armed Islamists, who stormed an upscale hotel in the Indian city, Mr. Whittam told the court.

While the prosecutor’s opening statement was public, most of the rest of the trial is subject to court-imposed restrictions that limit what can be reported.

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.

This trial will have unprecedented restrictions, however, with only a select group of journalists allowed to attend much of it, but not able to report on what they hear until after the verdict. Other parts will be held with no journalists allowed at all. The trial is expected to last six weeks.

The trial comes amid a heightened concern about terrorist activity in the U.K. from foreign fighters returning to Europe from Syria.

On Tuesday, police arrested three men and three women in southeast England, in Portsmouth, Farnborough and Greenwich. A spokesman for Thames Valley Police said the arrests were related to terrorism-related activities planned in relation to the conflict in Syria. No charges were immediately filed.

Separately, counterterror police arrested three men in central London as part of a continuing investigation into Islamic extremism and Syria-related terrorist activity that saw five other men arrested last week.

The men, all in their early 20s, are suspected of involvement in the commission, preparation or instigation of terrorism, according to London’s Metropolitan Police, known as Scotland Yard, which has called the case serious.

The plot appeared to be related to Islamic extremism but was at the early stages and didn’t seem to be sophisticated, officials have said. A number of residential addresses and vehicles were searched in West and Central London as part of the investigation. Six of the men remained in custody as of Tuesday afternoon in the U.K., and two had been released.

British authorities in August raised the country’s assessment of the level of the threat from international terrorism for the first time in three years. It is now at “severe,” the second highest on a 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, Prime Minister David Cameron said the threat from Islamic State “is a greater and deeper threat to our security than we have known before.”

—Cassell Bryan-Low contributed to this article.

Write to Alexis Flynn at alexis.flynn@wsj.com