A 43-year-old man was arrested in Braintree, east of London, after reportedly walking into a mosque with a knife shortly after news broke of the London murder.
Local lawmaker Brooks Newmark wrote on Twitter: "Local mosque in Braintree attacked by man with knives and incendiary device. Man arrested. No one injured."
Elsewhere, a man was in custody in Gillingham, south east England, on suspicion of racially aggravated criminal damage to a mosque, a Kent Police spokesman said.
Eyewitnesses to the horrific London attack described how the two suspects set upon a man in the street in broad daylight with knives and a gun.
They then stayed at the scene, asking passers-by to photograph and film them.
Armed police shot and wounded the two attackers after being called to the incident in Woolwich, south east London, by bystanders.
Prime Minister David Cameron has said the attack appeared to be terror-related.