It sounds like your router is failing to connect properly to your ISP's DNS server. That's the computer which converts a typed URL into the 'numeric' address of the website you require, sometimes called a 'dotted quad'.
Here's a test:
Enter amazon.co.uk into your browser's address bar, to see if you can get into the Amazon website. (Based upon what you've told us, I'll assume that you cant). Then enter 178.236.4.29 into the address bar, and try again. (That bypasses the DNS server, since you've provided the required doted quad yourself). If you get into the Amazon site, it's definitely a DNS problem.
If so, please tell us the make of your router and which ISP you're using.
Chris