On the flip side there are companies that would be reluctant to recruit people who did not study a modular course, and would not even consider anyone straight out of an integrated course. Integrated courses are not intended to produce rounded pilots. They train airline FOs. There are many interesting flying jobs out there for which that is not appropriate.
Overall those companies probably hire more low-hour pilots than BA, at least for the foreseeable future!
Incidentally I knew people who were interviewed by BA at the end of their modular course, so at times they have at times had no firm policy against such recruitment. Who knows what will happen when they next start to recruit low-hour pilots?