Yes definately. Usually through a private landlord but sometimes even through a letting agency. One of my mates has bad credit so they advised the letting agent of this who checked with the landlord whether he would be prepared to accept them as tenants. Luckily he said yes!
If you have a problem or get rejected because of a bad credit record then you can offer to pay more months rent upfront or offer a person to stand as a guarantor.
There are however a lot of tenants out there now looking for properties to rent so most landlords will be more picky with who they choose.