A Ukrainian student has pleaded guilty to trying to incite a race war on Britain's streets by launching a terrorist campaign in which he stabbed a Muslim grandfather to death and exploded bombs near mosques in an attempt to murder and maim worshippers.

Pavlo Lapshyn, 25, admitted to police that he hated anyone who was not white and that he wanted to carry out a series of violent attacks to convulse community relations.

His campaign started in April 2013, just five days after his arrival from Ukraine, where he had won a prize to gain work experience in Britain. When the PhD student was arrested in July, hours before it was feared he could strike again, police found three partially assembled bombs in his Birmingham flat.

His campaign caused alarm at the top levels of the British government, with the domestic security service MI5 joining the police-led hunt.

Lapshyn's bombing campaign started after the murder of Fusilier Lee Rigby in a London street, with his final explosive detonating weeks later on the day of Rigby's funeral – although police believe the campaign was not motivated by the murder of the soldier. It is believed the Ukrainian acted alone and was unconnected to any group.

On Monday,Laphshyn yesterday pleaded guilty at the Old Bailey in London to the murder and staging the bomb attacks, after confessing to them during police interviews. He will be sentenced on Friday.

The student stabbed Mohammed Saleem, 82, to death in Birmingham as he walked a few hundred yards from a mosque to his home.

Mohammed Saleem, who was stabbed to death as he walked home from the mosque in April. Photograph: PA

During police interviews Lapshyn confessed when asked about the murder: "I have a racial hatred so I have a motivation, a racial motivation and racial hatred." Police say he did not mention Muslims or a specific hatred of Islam.

After the guilty pleas, Shazia Khan, Saleem's daughter, said of her murdered father: "He was targeted simply because of his faith. His beard and his clothing represented who he was. To kill someone because of what they look like and what they believe in is unforgivable."

After the murder Lapshyn acquired materials for bombs. By June he had started placing homemade explosives outside mosques on Fridays, the main day when Muslims attend places of worship.

The device he planted in July, which had 100 nails wrapped around it to maximise the carnage, was aimed at worshippers at the Tipton mosque, where 300 were people expected to attend prayers.

But prayers that particular Friday were held one hour later, so mass casualties were avoided. The device was so powerful it left nails embedded in tree trunks, police said.

The search for Lapshyn was the most intense hunt for a serial bomber on the British mainland in years.

Assistant Chief Constable Marcus Beale, head of the West Midlands counter-terrorism unit, said Lapshyn was "self-radicalised" and used the internet to learn how to make bombs. After his arrest Lapshyn told police he "would like to increase racial conflict" and felt a series of explosions would achieve more than one big attack.

He was explicit about his motivation for the Tipton mosque attack in an interview recorded after he was cautioned: "The purpose was to commit a terrorist act."

Detectives who interviewed him described him as "calm and calculated". He even told police he carried out an attack near the mosque in Wolverhampton, which they had previously been unaware of.

After the verdict the home secretary Theresa May said: "This is a satisfying outcome to a highly distressing case where Pavlo Lapshyn's hatred has robbed a family of a loved one and attempted to cause fear and division within our communities."

Some in Muslim communities felt the attacks were under-reported in the media because Islam was the target, a view shared at one point publicly by West Midlands deputy chief constable David Thompson. Today Beale said "both the media and ourselves should reflect".

Lapshyn had been a gifted student who was studying for a PhD in machine building. Social media pages belonging to him contain extremist rightwing and Nazi material. There were images of Timothy McVeigh, whose bombing of a US government building in Oklahoma in 1995 killed 168 people.

Ukrainian researchers say Lapshyn's social media pages also contain material relating to Hitler, about contemporary Nazis, and rabidly antisemitic material. A laptop seized by British police contained an extremist rightwing publication, The Turner Diaries, also believed to have been read by McVeigh.

Further extremist material was found on Lapshyn's laptop, plus details of planning and virtual reconnaissance for the attacks. There were bus timetables to get him to the mosques he attacked, as well as press coverage of Mohammed Saleem's murder.

Police say they found no material belonging to British racist groups such as the British National party or the English Defence League. Nor was there material suggesting his bombing campaign was incited by the terrorist murder of Lee Rigby on 22 May, which occurred a month before Lapshyn's first bomb attack.

Lapshyn came to Britain after winning a competition to work at a software firm in Birmingham. At a prizegiving ceremony he stood next to the British ambassador to Ukraine.

Police say their inquiries showed no links to groups in Ukraine. But police there had arrested and fined him after an explosion in his flat in Dnipropetrovsk, Ukraine, which may have provided clues for his later actions.