And they do integrated, I know because I've been looking at loads of school and they go through every single rating and qualification required to become a frozen ATPL. the only extra is the 2 weeks IR conversion.
In which case I'm afraid they're not integrated - going through every rating & licence required to end up with a CPL/IR with ATPL knowledge is the modular route, especially if it ends up with an IR conversion required. The integrated route is 0-CPL/IR in one course.