Integrated may open to the door to BA with 200hrs, it may not. It's arguable that an integrated course may give you a slightly greater chance of getting into one or two other airlines with a low hours CV.
What is indisputable is that an integrated course is the far more expensive option, and that the modular route gives you great flexibility to train full time or part time, and to speed up or slow down your schedule to suit your circumstances and - just as importantly, the job market.
I could just about make a case for starting modular training at the moment, assuming you worked full-time and trained / studied for the PPL and ATPL writtens in your spare time. Taking it slowly and working on a 3 year schedule, there's at least a chance that the job market will look at lot better in 2012. If it's still bad you can always delay the CPL & IR.
For what it's worth, I think it would be madness to sign up for an integrated course at the moment.