is that if you buy one of these machines you will have exactly the same level of consumer protection as you would if you bought a brand new computer. The law makes no distinction in terms of your rights.
Secondly, these reconditioned machines have all been returned to PC World within 28 days of the original purchase, and have been thoroughly checked over by a manufacturer's approved refurbisher. The hard drive is guaranteed to have been cleansed of all data, and the computer will be in a manufacturer's box, complete with all accessories etc. To be honest, it would be very hard to tell that the computer isn't new.
Provided that you understand the computer will have been used slightly you should have no hesitation in buying. Whether your choice is worth the money is a matter for you to decide, but I certainly wouldn't have any hesitation in buying one of these machines.