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A Muslim convert described as "a dangerous individual" has admitted plotting to kill around 100 people outside a Disney store on London's Oxford Street.
The Old Bailey heard how Ludlow, 26, swore allegiance to Islamic State as he plotted to mow down shoppers in March.
He researched potential targets including St Paul's Cathedral, the Disney Store and Madam Tussauds, and also van rental and hotel accommodation.
He then wrote down his intentions in a letter, which was found ripped up in a bin.
Ludlow was charged after being arrested in Rochester on Wednesday, April 18 this year.
The resident of Warren Wood Road in the town had been charged with two counts of engaging in conduct in preparation for acts of terrorism.
That is contrary to Section 5 of the Terrorism Act 2006. He also faced one count of arranging funds or property for the purposes of terrorism contrary to Section 17 of the Terrorism Act.
He pleaded guilty to one act of terrorism and the other act of terrorism is to remain on file. He also pleaded guilty to the count of arranging funds for terrorism.
He appeared at the Old Bailey in London this afternoon, and a provisional date for his sentencing has been set for November 2.
Speaking afterwards, Det chief supt Kath Barnes, head of Counter Terrorism Policing South East, said: "Ludlow was planning an attack in the UK after he had sworn an oath of allegiance to Deash.
"Ludlow had gone as far as writing out attack plans and conducting reconnaissance of potential targets.
"An investigation led by detectives in Counter Terrorism Policing South East working closely with Kent Police led to Ludlow being stopped before he was able to finalise his plans to carry out an attack.
"We are pleased with his guilty plea, which demonstrates the quality of evidence gathering by detectives working on this investigation.
"Ludlow was a dangerous individual and I have no doubt that the public will be much safer as a result of our actions."
Police say the threat to the UK from international terrorism remains "severe", meaning an attack is highly likely.
They have urged the public to remain vigilant and report any suspicious behaviour or activity in confidence on 0800 789 321 or visit gov.uk/ACT/ or 999 in an emergency.
In the event someone gets caught up in a weapons attack they are urged to follow the Run, Hide, Tell advice and follow @TerrorismPolice for updates.