The mortgages are available to those who have successfully started a business but only hold one year of financial records.
Both are 2-year mortgages and are also available for remortgages and additional borrowing.
Liam Flaherty, underwriting manager at The Cambridge, said: “We saw anecdotal evidence of the self-employed being hit hard by the COVID crisis.
“The self-employed appear to have experienced a greater drop in earnings, compared to employed workers.
“As experts in homes and housing, being a responsible lender and a support to local communities, we felt we needed to offer products that made it easier for this group to access funds for a home.
“I am not aware of other lenders offering this type of mortgage, and know that it will enable more people to access funds.”