I doubt that there is a database anywhere that tracks training route and employment stats for the entire UK or all of JAR land and is also accessible to the likes of Flyer. Perhaps the CAA have such data for the UK, but as far as I know, they don't even publish pass rates for exam and flight test data they do have. I suspect what they publish are statistics on how many people train modular and integrated, but that doesn't mean the employment rate matches that split. Even if 80% is accurate, it would be important to know what type of jobs are involved, how long it took to get them, how much self-improver work experience at various low wage jobs was involved, and how many were SSTRs or pay-to-fly types, etc.
Finally, even if the statistic is accurate and otherwise meaningful, it says nothing about how many from either route don't get work. Given that there are four integrated approved schools and about 90 approved for modular, I would be more comfortable having the failure stats than the success stats, even if I accepted the 80 percent figure.
To modify what RickO says about 75% of statistics being made up, I would add the other 25% need a lot of caveats to be properly deployed for meaningful risk management.