Dr Imran Farooq was stabbed outside his home in Green Lane, Edgware, last year.
His killers may have had help from other people, some of whom could have assisted unwittingly, police added.
An e-fit image of a suspect wearing a baseball cap has been released. A man aged 34 who was questioned last year has been bailed until this November.
Dr Farooq, who was a senior member of the MQM party, was killed "in a brutal manner", said Det Ch Supt Neil Basu of the Metropolitan Police.
His death, on 16 September 2010, "has left the community with a deep sense of loss", he added.
The 50-year-old suffered multiple wounds and blunt trauma to the head.
Police have previously said he may have been followed by up to four Asian men in vehicles or on foot.
Officers are asking for information about Dr Farooq, who came to the UK in 1999 seeking political asylum, and his routine.
They also want to talk to anyone asked to help buy items which could have been used in the attack, of the planning of it, such as knives or mobile phones.
It is thought two kitchen knives were used in the attack, along with a brick from a house.
One of the knives was made by Ausbein Messer, with a 5in (13cm) blade, and the other was branded as Schinken Messer, with a 5.5in (14cm) blade.
The murder of a Pakistani politician in north London a year ago was "carefully planned", Scotland Yard has said, as it offered a £20,000 reward for details.