The Tories won Redbridge from No Overall Control with the gain of 10 seats to Labour's loss of seven.
Cllr Laugharne was elected deputy leader and cabinet member for regeneration in 2000.
Mr Javed said:
'For seven of the last eight years Labour has been the minority administration and we have done much to improve services and to empower local people to play a vital part in shaping the decisions that affect them.
'It is time for a new team to carry the leadership mantle and provide constructive opposition to the Tories. We will listen and consult the people of the borough and I shall play a full part in working towards a Labour victory in 2006.'
Mr Laugharne said:
'The changes that Labour put in place have made the council more open and democratic and transformed Redbridge into one of the best performing authorities in the country. The Tories must not be allowed to turn back the clock to the bad old days prior to 1994, when decisions were made by a hand-full of councillors behind closed doors.'