Modular can be done just as fast as integrated.
It took me exactly 24 months from my PPL skill test to my IR test, and I waisted at least 6 months mucking about with where and how to do my ATPL's, and I lost about 2 months due to bad weather to complete my IR. So I could have done all in 14 months, add to that I had a wife, 6 month old baby and a business to run, so was not able to study full time all the time!
By the way, all first time passes in all, and averages 95% on my ATPL's, so it is possible to do modular fast, and it cost me in total around £29.000 for CPL/IR/ME and ATPL's.
I had some hours from before. Went few hours over, due to all the above circumstances, but all comes down to your own dedication and hard work.
With the money I saved, I could pay my own TR, while I see loads of Oxford guys now spending top money on their course and then pay TR at Ryan air, it will cost you a fortune in the end, I could do the same, for half the price.