Sandwell Council bosses say a large family has already been re-housed in the borough by Newham Council.
Meanwhile Brent Council has also contacted the Black Country council to enquire about placing tenants in privately-rented homes.
With concerns more local authorities in the capital could follow suit, councillors in Sandwell claim the High Court ruling over council tax last summer is behind the issue.
In that ruling, the judge decided a requirement for residents to have lived in Sandwell for two years before they could claim council tax support was illegal.
Deputy council leader Councillor Steve Eling said: "Within just weeks of the court's judgement that deemed there was no evidence of people being relocated from London to Sandwell, a London borough has placed a family here, and another has confirmed it will be dumping poor families in Sandwell, apparently taking advantage of cheaper rent here.
"This is a direct result of the court's judgement in the case of Brent Council, and would appear to apply equally to the others. As a result, we're powerless to stop this happening."
Councillor Eling said the moves by the London authorities will burden Sandwell residents, as they will have to pick up 100 per cent of the council tax bill for these families, as well as those that have already been placed here.
"That's why we introduced the two-year residency rule in the first place, to protect Sandwell taxpayers and Sandwell families who are most in need," he said.
"We decided only to offer a reduction in council tax to people who had continuously lived in Sandwell for two years.
"Unfortunately following the court's judgement, we've had no choice but to suspend that policy."
He says discussions over the policy are continuing with the Government as the council face a £1.6 million shortfall covering the cost of council tax discounts.
The council has already launched a consultation over how it should cover this shortfall.
Councillor Muhammed Butt, Leader of Brent Council said: "We have made contact with Sandwell MBC's housing department to let them know that we are seeking to secure properties within their borough. We hope the number of families involved will be small."
A Newham Council spokeswoman added: "We can confirm that we have recently helped a Newham family find accommodation in Sandwell and we have notified Sandwell Council. Due to the Government's welfare reforms, London is now unaffordable for many so Newham Council has been forced to look outside the capital to find suitable accommodation for a small number of its homeless families."