(2-part post):
You've not said how long you've had the printer. It could make a difference. If we can forget about the warranty for the moment, here are your rights:
(i) if the printer was found to be defective before you'd legally 'accepted' it (i.e. as soon as you got it home or very shortly afterwards), you're entitled to a full cash refund from PC World;
(ii) if you've 'accepted' the printer but less than 6 months has passed since the date of purchase, the law assumes that the breakdown was due to an 'inherent fault' (e.g. poor quality components or poor workmanship) unless there is clear evidence to the contrary. (e.g. if it's obvious that the printer has been under a road roller you can't claim that it's an 'inherent fault'!). In this case PC world must either replace the printer or repair it. (They have the discretion to choose which remedy to apply) ;
(iii) after the 6 month period, you continue to have the right to demand that PC World replace or repair the printer, up until 6 years after the date of purchase, if a breakdown occurs which was due to an inherent fault. However, there is no longer an automatic assumption that any such breakdown is due to an inherent fault. It is for you to show that, based on the balance of probabilities, this was the most likely cause.