I would never give up on the non integrated route. After all, CTC isn't integrated.
Any way, they are in a slightly different category.
Modular won't go away. Many operators are looking for pilots that haven't been through a factory. The most interesting jobs aren't usually advertised, you do have to seek them out. Use a bit of initiative and find them.
Always remember that airlines have a quota set by the UK CAA of low houred pilots to experienced pilots. Therefore, if airline X takes most of it's low houred guys from eg CTC etc, then by all means have a go but look at that airline once you have some experience.
How you get that experience and what that experience consists of is up to you. Instruct, drop parachutists, night freight, Africa, charter work. None of this will fall into your lap. You'll have to chase it down.
Good luck.