Mrs Hodge proposed a 'transparent' points-based system where families who have lived in Britain for longer and have contributed more to national insurance are more likely to be given council housing as a result.
Chief executive Adam Sampson said:
'The failure to build new homes and the devastating impact of the Right to Buy leaves the small amount of social housing stock vulnerable to being exploited for political means.
'These comments perpetuate the myth that social homes are given to new immigrants coming to the UK at the expense of the indigenous population - when in fact homes are allocated by balancing what people are entitled to against immediate housing need.'
The Egyptian-born politician wrote in the Observer that such measures would 'promote tolerance rather than inviting division'.
Margaret Hodge 'A message to my fellow immigrants'
But immigration agency the Refugee Council has accused Mrs Hodge of aligning herself with British National party (BNP) policies.
In her Observer interview the minister said that 'difficult questions' such as this needed to be raised, insisting that 'at present we prioritise the needs of an individual migrant family over the entitlement that others feel they have to resources in the community'.
'We should look at policies where the legitimate sense of entitlement felt by the indigenous family overrides the legitimate need demonstrated by the new migrants,' she continued.
According to the Barking MP only a 'small number' of refugees have the same housing entitlements of British citizens.
But the Refugee Council's head of international and UK policy, Nancy Kelley, responded: 'The way to counter some of the views put forward by far-right parties is not to follow their lead.'
Shadow immigration minister Damian Green said that Mrs Hodge's comments were an admission of the 'long-term failure of this government to control immigration'.
'This is why Conservatives are calling for an explicit annual limit on the numbers coming here from outside the EU so that we can avoid exactly the sort of problems she is talking about,' he added.
Mrs Hodge was criticised in the run-up to council elections in 2006 by speculating that eight out of ten white families would consider voting for the BNP.
The far-right organisation went on to become the second-largest party on Barking and Dagenham LBC.
Policy & politics