A total of 18 families from London with housing problems have been moved to Telford & Wrekin in five years.
It is claimed they are being relocated by London borough councils that would otherwise have to pay high rents through housing benefit, often offering cash incentives to move.
The practice was today condemned by campaigners as 'social cleansing', with low-income families being forced out of their communities and made to live in areas where they have no ties.
The typical average rent in London borough for a family is £2,885 a month, more than five times that of Telford.
Figures obtained by the Liberal Democrats under the Freedom of Information Act show that seven families from London have been allocated council properties in Telford. The remaining 11 have been housed in private rented accommodation. They also show that 15 families were moved to the Shropshire borough in the space of a single year.
The Liberal Democrats claim the policy is having an impact on social housing waiting lists.
The figures show that in 2016/17, five families were given council social housing in the borough, having been moved from the London borough of Harrow. In 2013/14, one family from the the borough of Redbridge was given social housing in Telford & Wrekin, and in 2015/16 one family from the borough of Brent was rehoused in the area.
Of those moved into privately rented accommodation in 2016/17, 10 were moved from the borough of Hounslow, where the average rent is lower than most in London but at £1,300 per month is still more than double that of Telford. The other was moved from Brent in 2014/15.
Liberal Democrat spokesman Ian Jenkins said: "We are seeing a version of social cleansing where the poorest and must vulnerable are kicked out of London, uprooted and dumped in Shropshire. This is frankly scandalous. It is putting pressure on our vital public services in the country."
Councillor Shaun Davies, leader of Labour-run Telford & Wrekin Council, agreed there was a problem and said it was something the council had been concerned with for some time.
He said it was not unique to Telford, and affected a number of local authorities in the West Midlands.
"It's a growing issue for authorities in the Midlands," he said. "The south-east is not building enough affordable housing. It is not just London, there are many areas in the south-east which have massive housing lists, and people are making the decision to move.
"We're not against people moving around the country, but it needs to be done in a controlled, joined up way."
Councillor Davies said he had written to a number of London boroughs asking them to clarify their position, and had received a mixture of responses. He said in many cases private companies acted as intermediaries and gave landlords in Telford incentives to provide homes for people.