My mistake, the 7 years is correct if your coming through the normal EASA pathway. ie. you have to hold a CPL/IR/MCC in order to get the ATPL. I believe the 3 years your talking about refers to CPL and IR.
So I don't know for sure how long I get to convert my license, it doesn’t appear to be in CAP 804 but I would assume it's at least 3 years