Ive currently got a long blue cable running through the middle of my front room - up my stairs and over the bannister into my housemates room - It looks horrible.

Right anyway ive drilled a hole through the living room celing into his bedroom and brought some trunking to keep it tidy

but i cant drill a hole big enough for the bit that clips into the newtwork part of the router and PC. Is there a way or a network cable that can be brought where its able to change - remove the end so i can fit it through the hole?

Cant you just cut the connector/plug off and then rewire it? I remember doing this before at a mates house, it isn't actually that difficult. If you're unsure just ask google, it nearly wins all the time 100% of the time!

The problem with re-wiring it is you'll probably need a crimping tool (and a cable checker if you want it done right), you could do a bodge job and slice the cable and use a cake block to put colour to colour back, but you may lose some connectivity and tbh I've never tried it (as I have the aforementioned tools at work) best bet is to find someone you know with the tools and pay them in beer

Bigger drill bit?

lol - bigger drill bit not really an option as the hole and the entry and exit points are in pretty tight locations with not a lot of give

Shake the drill bit around in the hole to make it slightly bigger/ crimp the cable like reo said. MAN UP!

Something like this then?

Ill have to check out Wilkos tomorrow - but im guessing any crimpers will do tho right?