You probably can't.
Amazon usually use standard 1st class postage, which means that there is no tracking available. This is because they have no barcodes and with 82 Million items handled each day, it'd be impossible to maintain a complete tracking service.

HOWEVER, sometimes Amazon uses Royal Mail Recorded Delivery or Special Delivery. If this is the case, they will send you a tracking number for you to put into the Royal Mail website.

95% of the time though, its standard first class, so there's no tracking.