Both American and British dictionaries list “dirt-cheap”. When you say that you bought something “dirt-cheap” what you are implying is that you bought it extremely cheap; in other words, the thing you bought was as cheap as dirt.
*Savithri managed to get the house dirt-cheap. *The young couple sold me the car dirt-cheap.
The word “dead” is used in British English in informal contexts to mean “very”. Therefore it is possible to say that something was “dead cheap”. It can be used with other words as well.
*I wouldn’t buy that house even if it were offered to me dead cheap.