The statue of Sir Winston Churchill in Parliament Square in Westminster was defaced overnight with "Zionist war criminal" and other graffiti.
A 38-year-old man was arrested on suspicion of racially aggravated criminal damage.
In an update, the Metropolitan Police said he has been further arrested on suspicion of supporting Palestine Action, which is a proscribed organisation, under the Terrorism Act and remains in custody.
A No 10 spokesman said of the vandalism: "It's obviously a disgrace. It's completely abhorrent.
"Churchill was a great Briton. This Government will always stand up for our values and the perpetrator must be held to account.
"We're glad the police have made an arrest."
Officers from the Met Police were alerted to the vandalism shortly after 4am on Friday.
The statue has been cordoned off and was being cleaned this morning.
A Greater London Authority spokesperson said: "We are appalled by this vandalism to the statue of Sir Winston Churchill and work is under way to remove the graffiti as quickly as possible."
Commenting on an image of the monument, which was shared on X, Dave Rich, director of policy for Community Security Trust, posted: "Free Palestine" and a Hamas red triangle, if you zoom in close enough. This extremism is never just a threat to Jews."
Read more from Sky News:
Netflix withdraws Warner Bros bid
We are in a new era of multi-party politics
The Jewish Leadership Council said it was "disgusted" by the defacement of the statue.
It said on X: "In targeting the statue of a British hero who led this country in the fight against the Nazis, the perpetrator has found a perverse way to combine a hatred of Jews with a disdain for Britain."
Phil Rosenberg, president of the Board of Deputies of British Jews, wrote: "One of the greatest champions for liberty, who defeated the Nazis, defaced.
"Zionism, the national liberation movement of the Jewish people, inverted.
"Santayana's 'Those who cannot remember the past are condemned to repeat it', never truer."
The 12ft-tall statue on the north-east corner of the square, created by Ivor Roberts-Jones, was unveiled in 1973 by the former prime minister's wife, Lady Clementine Churchill.
It is one of 12 statues on or around Parliament Square, most of well-known statesmen such as Nelson Mandela and Abraham Lincoln.
The former prime minister's statue has been vandalised several times over the years, including during demonstrations.
Last December, both the Metropolitan Police and Greater Manchester Police announced anyone chanting "globalise the intifada" would face arrest.
The decision by the two police forces came in the wake of the Bondi Beach terror attack, and the terror attack at Heaton Park synagogue in Manchester on 2 October.
(c) Sky News 2026: Man arrested after 'completely abhorrent' vandalism of Churchill statue
Gorton and Denton by-election result proves Polanski surge is real and the Greens are a serious threat to Labour
Man who left his partner paralysed after she told him she was leaving is jailed for 16 years
Afghan migrant jailed for raping 'vulnerable' woman
Picture of 'rare' boot released as police try to identify woman's body found off Iona coast
New legal action planned over proposal to house 540 asylum seekers in Sussex town
UK issues travel warning as Middle East crisis worsens
Murderer jailed for inflicting more than 100 injuries on partner after plying her with vodka
Soham murderer Ian Huntley remains in a serious condition after prison attack
