This is not yet confirmed officially, but multiple sources are reporting that the London attacker is someone well known to police and security services. He is an Islamic cleric named Abu Izzadeen aka Trevor Brooks, born in the UK.
La Stampa, one of Italy's largest news outlets, is also identifying Izzadeen as the attacker.
"18.55- Il sospetto terrorista si chiamerebbe Abu Izzadeen (Trevor Brooks), imam di Clapton, un quartiere nella zona est di Londra e considerato un «predicatore d’odio». È un cittadino britannico di origini giamaicane, di 41 anni, nato il 18 aprile 1975 a Hackney, zona londinese confinante con Clapton.
The suspect terrorist is named Abu Izzadeen (Trevor Brooks), imam from Clapton, a quarter in the east zone of London and considered a "hate preacher". He is a British citizen of Jamaican origin, 41 years old, born 18 April 1975 in Hackney.
*Update: (Zero Hedge) The above reports are being disputed since Brooks is reportedly still in a British prison.
This should be cleared up today.