Many young families are now unable to buy in the area because of low incomes and rising prices.
Gordon Brown has called on councils and housing associations to meet his goal of building 3m new homes over the next 13 years.
Mr Bradshaw said housing was now at the top of the government's agenda.
He said councils in parts of the region where there was pressure from second home owners would get more money for social housing.
He told BBC South West's Politics Show: "We shall have to wait until the Comprehensive Spending Review, but housing and planning are all coming together.
"I am optimistic that there will be more funding for it."
He said that green field sites were not off-limits for housing, but councils would be encouraged to seek out previously developed sites.
Government figures now put the cost of the average house in the South West at £218,495, and show house prices in the region rose by 9.8% in a year.
In many rural districts average house prices are more than 11 times average local earnings.
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