airlines have a preference for integrated students over modular. Its not right, but its the way it is.
A very misleading an inaccurate generalisation, whatever you've read on pilotjobsnetwork.com.
The UK's four biggest employers of pilots are BA, Ryanair, Easyjet and Flybe. Regarding low-hours pilots, BA will only take those from an integrated background, we know that. Easy have a well-trodden route via CTC, which presumably they are happy with.
Ryanair on he other hand couldn't care less where or how you got the licence, providing you can pay for a type rating. Flybe are more than happy to take modular candidates.
That's the big four taken care of, and for every operator that takes a small number of low-houred pilots by picking up the phone to Oxford or FTE, there's another that is perfectly happy with modular CVs (e.g. Jet2, Air Southwest, Eastern, Aurigny, etc etc).