In 20 days you will be able to learn how to be a good 'house bashing' electrician. You will be able to wire in sockets and the like but not really understand the fundamentals. That aspect of electrics isnt hard.
On the other hand, passing all of the city and guilds exams in that time with minimal knowledge is slightly optimistic. I dont know the extent of these courses though.
Part p is the electrical part of the building regulations. Anyone can print it off online. An exam for part p is just like the 17th edition exam, it tests your knowledge of the regulations, thats all.
To become a certified electrician and to be able to 'write off your work' you ideally need to be part of a scheme like Napit, NICEIC etc. OR consult the local council on your domestic electrical installation, every time you add to it (there are a few 'loopholes' though).