Hundreds of police officers are working on the probe into the London terror attack.
Scotland Yard's acting deputy commissioner, Mark Rowley, described the attack in Westminster as 'horrific' and said in addition to the killer, three others died and seven casualties were critically injured.
He said hundreds of police officers worked through the night and extra officers have been drafted in today, with annual leave cancelled.
The police chief said: "Greater clarity is now developing regarding the casualty figures as we have now collated information from the public and five hospitals - the latest figures I have are that there are currently four dead and 29 people were treated in hospital.
"We are still collating numbers of walking wounded and of those in hospital sadly seven of them are in a critical condition.
"The fourth man of course was the terrorist who was shot dead by armed police at the scene.
"Hundreds of detectives have been working through the night and during that time I can confirm we have searched six addresses - and made seven arrests. The inquiries in Birmingham, London and other parts of the country continue.
"It is still our belief - which continues to be born out by our investigation - that this attacker acted alone yesterday and was inspired by international terrorism.
"To be explicit - at this stage, we have no specific information about further threats to the public.
"Clearly our investigation is ongoing - developing all the time - and is focused on his motivation, his preparation and associates.
"The large and complicated crime scene remains in place and our work there continues - I would like to thank everyone for their support and patience as we finish this work.
"As people are out and about on the streets of the capital this morning they will see more police officers on duty - armed and unarmed - and a mix of British Transport Police and the City of London.
"We have cancelled some leave and increased some duty hours and are working to make sure that we can out in force to reassure the public.
"We must not allow terrorists to create discord, distrust and fear.
"The police stand with all communities - later today a meeting of faith leaders will be held here at New Scotland Yard.
"Whilst our work to investigate and understand what happened yesterday continues with vigour - we must also reflect.
"I want to thank the public for their support and all their good wishes - I know it is appreciated by all those men and women who are out there today protecting us.
"Finally, I would also like to ask the public for their continued help and continued vigilance and if you see anything that causes you concern or raises your suspicions do not hesitate to call us - 0800 789 321 - or in an emergency 999."