Yes, don't bother messing around with Sony. Get straight back to Waterstones, explain the situation to them, and tell them that you want them to repair or replace it for you (which they are legally obliged to do).
Also make a big deal of the fact that it's only a week old, and that it's their responsibility to prove this fault was not inherent in the product from the off because it's less than 6 months old.
These are all your rights under the Sale of Goods Act (SOGA). If they try to refer you to Sony, refuse to go to them - the contract is with Waterstones, the retailer, not Sony, the manufacturer, so it's their responsibility to sort it out.
The law says that you don't have to produce a receipt (although obviously it helps), so don't let them fob you off on that front, either...particularly as they're pretty much the only licensed UK seller of Readers anyway!
I only know about this because I had a series of massive rows with Argos when they refused to replace my broken 4 month old Xbox 360 Elite. They were essentially trying to dodge giving me a replacement because of the well known manufacturing faults with the console, and were very stubborn in saying they couldn't help, and that I should go to Microsoft.
After getting no joy from the store or their customer service line, I wrote a letter to the Chief Exec of the Home Retail Group (which owns Argos), telling them that unless they fulfilled their obligations under SOGA, I was going to take them to court. Result? The day after the letter was delivered, the Chief Exec's personal secretary called me at home, and told me to send the Xbox to her directly, as she'd been authorised to give me a full refund
The one thing I learned from that debacle is to never, ever, EVER let a company con you out of your rights.