So these pages have been appearing when I try to go onto Google, Facebook, and now even Soompi.
It's a different page for each, but in order to get onto the website, I HAVE TO clear my cookies.
Is there any way I can fix this? It's really annoying me

400 bad requests are most commonly caused by URLs sent by your web browser that the receiving end (server) cannot interpret. This can be caused by a multitude of things such as, a corrupt browser or a bad DNS server. What browser are you using? I assume this started recently? You can attack this in two ways (software/hardware).
Software:
IF you're using Firefox, maybe you installed an extension recently that is causing the browser to be unstable?
IF you're using IE, then it's more than likely being caused by some type of Spyware corrupting it.
Download and run Spy-bot Search and Destroy. This should detect and clean most of the infections on your PC. It's free, and it also includes realtime protection. You can find it here > www.safer-networking.org
http://www.malwarebytes.org/mbam.php < This is also another good tool for removing Spyware/Adware, however, it is not free.
Hardware:
Unplug the power from your cable/dsl router and plug it back in. Also powercycle your router (assuming you have one) to reset it i.e. unplug the power and plug back in. Linksys routers are notorious for doing this. I'm not a fan of Linksys products.
From my experience, I've seen spyware and routers cause this behavior. Powercycling your router may fix it, but it never hurts to check your computer for Spyware.
Hope this helps.