It is definitely doable, however the CPL itself if done full time will not last more then 4 -5 weeks, and in that sense you will probably be able to do it a good deal cheaper.
I found that the CPL was not to heard, but you need continuity and currency to deal with unusual attitudes, timed turns. If you choose wrong time of the year you will be cursing for half the period.
Now is the best time to do it, come autumn, and UK weather is hell.
I would rather take holidays and do it intensively then spread it out to long. End of the day it is a little more advanced then PPL, so you will be surprised how fast it goes.